2006-12-04 06:40:06 · 9 answers · asked by lntpixie 1 in Science & Mathematics ➔ Mathematics
GIVEN:
10x - 3 = 8x²
SOLVE:
For the value of x.
First, set the equation = 0, Bring all of the other term(s) to the side with the (+x²)
By using the "opposite" opperation to BOTH sides of the equation to move each term seperately.
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SOLUTION:
10x - 3 = 8x²
10x - 10x - 3 = 8x² - 10x
- 3 = 8x² - 10x
CONTINUE to set the equation = 0, by using the "opposite" opperation to BOTH sides of the equation.
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- 3 = 8x² - 10x
- 3 + 3 = 8x² - 10x + 3
0 = 8x² - 10x + 3
I prefer the variables on the LHS. So, let's switch sides!
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THEREFORE:
8x² - 10x + 3 = 0
Now, let's factor the TRINOMIAL!
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8x² - 10x + 3 = 0
Multiply 1st and 3rd term together to get (+24x²).
Factor (+24x²) into two factors whose sum = the middle term of (-10x).
1x X 24x
2x X 12x..................Oooops! I thought these were the factors.
3x X 8x................. Keep going!
4x X 6x................BINGO!
(-4x) + (-6x) = -10x & (-4x)(-6x) = +24x² .......Yea!
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This is a really kewl factor by grouping trick, I LOVE it!
Bring down the first term of: 8x²
Next, write the SMALLER of the two factors 1st: -6x
Followed by the LARGER of the two factors: -4x
Finally, bring down the third term of: +3
8x² - 6x - 4x + 3 = 0
Now, lets factor by grouping!
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Factor out the GCFs.
GCF#1 = 2x
GCF#2 = -1
(8x² - 6x) + (-4x + 3) = 0
2x(4x - 3) - 1(4x - 3) = 0
GCF#3 = (4x - 3)
(4x - 3)(2x - 1) = 0
SOLVE for "x" by setting each factor = 0 and using the "opposite" opperation to BOTH sides of the equation.
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(4x - 3)(2x - 1) = 0
4x - 3 = 0
4x - 3 +3 = 0 + 3
4x + 0 = 3
4x = 3
(4x)/4 = 3/4
x = ¾
2x - 1 = 0
2x - 1 + 1 = 0 + 1
4x + 0 = 1 ......................Oooop! I found my mistake!
2x - 1 + 1 = 0 + 1
2x + 0 = 1
2x = 1
(2x)/2 = 1/2
x = ½ ..................That's better!
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PREVIOUS ANSWER:
LET:
x = 3/2
CHECK#1:
10x - 3 = 8x²
10(3/2) - 3 = 8(3/2)²
10(3/2) - 3 = 8(3²/2²)
10(3/2) - 3 = 8(9/4)
(10÷2)[3/(2÷2)] - 3 = (8÷4)[9/(4÷4)]
5(3/1) - 3 = 2(9/1)
5(3) - 3 = 2(9)
15 ≠ 18 is a FALSE statement. Therefore, x ≠ 3/2
Time to go back and check our work!
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NEW ANSWER#1:
LET:
x = ¾
CHECK#2:
10x - 3 = 8x²
10(¾) - 3 = 8(¾)²
10(¾) - 3 = 8(3²/4²)
10(¾) - 3 = 8(9/16)
(10÷2)[3/(4÷2)] - 3 = (8÷8)[9/(16÷8)]
5(3/2) - 3 = 1(9/2)
(15/2) - (3/1) = 9/2
(15/2) - [(3)(2)/(1)(2)] = 9/2
(15/2) - (6/2) = 9/2
(15-6)/2 = 9/2
9/2 = 9/2 is a TRUE statement. Therefore, x = ¾
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LET:
x = ¼
CHECK#3:
10x - 3 = 8x²
10(¼) - 3 = 8(¼)²
10(¼) - 3 = 8(1²/4²)
10(¼) - 3 = 8(1/16)
(10÷2)[1/(4÷2)] - 3 = (8÷8)[1/(16÷8)]
5(1/2) - 3 = 1(1/2)
(5/2) - (3/1) = 1/2
(5/2) - [(3)(2)/(1)(2)] = 1/2
(5/2) - (6/2) = 1/2
(5-6)/2 = 1/2
-½ ≠ ½ is a FALSE statement. Therefore, "x" might ≠ ¼
Let's go back and CHECK our work, again. maybe I made a mistake along the way, somewhere.
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NEW ANSWER#2:
LET:
x = ½
CHECK#4:
10x - 3 = 8x²
10(½) - 3 = 8(½)²
10(½) - 3 = 8(1²/2²)
10(½) - 3 = 8(1/4)
(10÷2)[1/(2÷2)] - 3 = (8÷4)[1/(4÷4)]
5(1/1) - 3 = 2(1/1)
(5)(1) - (3) = 2(1)
5 - 3 = 2
2 = 2 is a TRUE statement. Therefore, x = ½
GOOD JOB!
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FINAL ANSWER:
x = ½ and ¾
Congrats on making it to the end with me! ♥
Good Question!
2006-12-04 06:58:14 · answer #1 · answered by LovesMath 3 · 0⤊ 0⤋
(we'll write it 8x^2)
So 10x - 3 = 8x^2 Rearrange and you get:
0 = 8x^2 -10x + 3 Break that up and you get
0 = (4x - 3)(2x - 1)
so either 4x-3 or 2x -1 (or both) = 0, so solving for x:
x=3/4 or x = 1/2
Plugging it back in, we find that both numbers make sense, so they are both part of the solution.
2006-12-04 06:50:35 · answer #2 · answered by theyuks 4 · 2⤊ 0⤋
10x-3=8x^2
8x^2-10x+3=0
(4x-3)(2x-1)=0
Now,solve for x
4x-3=0
4x=+3
x=3/4
and
2x-1=0
2x=1
x=1/2
means that in the equation, x is either 3/4 or 1/2 You can find out by plugging either of those into the original equation and seeing which one comes out 0
2006-12-04 06:48:27 · answer #3 · answered by Tony T 4 · 1⤊ 0⤋
10x-3=8x
2x = 3
x = 3/2
₢
2006-12-04 06:45:32 · answer #4 · answered by Luiz S 7 · 0⤊ 1⤋
By "to the second" I'm gonna take it to mean
10x - 3 = 8x^2
Move everything to the right hand side, to give you
8x^2 - 10x + 3 = 0
Now, factor.
(4x - 3) (2x - 1) = 0
Note: When factoring, you want to put in brackets the factor of 8x^2. 8x^2 is equal to 4x and 2x, so you'd have to do
(4x + ?)(2x + ?)
and do trial and error by testing factors of 3.
As a result,
4x - 3 = 0
2x - 1 = 0
4x = 3
2x = 1
x = 3/4
x = 1/2
2006-12-04 06:49:44 · answer #5 · answered by Puggy 7 · 0⤊ 1⤋
8x^2 - 10x + 3 = 0
(4x - 3)(2x - 1) = 0
4x - 3 = 0 or 2x - 1 = 0
4x = 3 or 2x = 1
x = 3/4 or x = 1/2
QED
2006-12-04 07:06:07 · answer #6 · answered by CSUFGrad2006 5 · 1⤊ 0⤋
10x-3=8x
+3
________
10x=8x
-8 -8
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x=2
2 to the 2nd power is 4
2006-12-04 06:46:18 · answer #7 · answered by kyrah aka babygirl 2 · 0⤊ 2⤋
(4x-3)(2x-1)
x=3/4 & 1/2
2006-12-04 09:41:47 · answer #8 · answered by Anonymous · 1⤊ 0⤋
(4x-3)(2x-1) = 0
x=0.5 and 0.75
2006-12-04 06:46:10 · answer #9 · answered by MustangGT 2 · 1⤊ 0⤋