Quadratic Equation Help?

Question

Find the solution(s) for x.

1. x(x – 3) = 0

2. x2 + 3x + 2 = 0

3. 9x2 – 12x = -4

4. 8x2 – 6x = 2

5. 2x2+ 5x = 0

6. x2 + 6x - 40 = 0

7. 2x2 + 2x = 28

Multiply the binomials.

8. (x + 3)(x – 5)

9. (3x – 5)(2x + 1)

10. (x + 4)(x – 3)

11. (x + 4)(x - 4)

12. (x – 5)( 2x + 5)

Answer 1

1. X = 0 or x = 3

2. (x + 2)(x + 1)
x = -2 or x = -1

3. 9x^2 - 12x + 4 = 0
(3x - 2)(3x - 2) = 0
x = 2/3

4. 8x^2 - 6x - 2 = 0
(4x - 1)(2x - 2) = 0
x = .25 or x = 1

5. 2x^2 + 5x = 0
x(2x + 5) = 0
x = 0 or x = -2.5

6. (x - 10)(x + 4) = 0
x = 10 or x = -4

7. 2x^2 + 2x - 28 = 0
x^2 + x - 14 = 0
x = (-1 +/- sqrt(1 + 56))/2
x = (-1 +/- sqrt(57))/2

8. x^2 -2x - 15

9. 6x^2 - 7x - 5

10. x^2 + x - 12

11. (x^2 - 16)

12. (3x^2 - 5x + 25)

Answer 2

to solve a quadratic equation set the equal to zero, factor the polynomial, and solve for x for each factor. I am leaving a few for you to do on your own.


1. x(x – 3) = 0
x=0
x–3=0 = x=3

2. x2 + 3x + 2 = 0
(x+2)(x+1)=0
x= –2
x= –1

3. 9x² – 12x = -4
9x²-12x+4=0
(3x-2)(3x-2)=0
3x-2=0 3x=–2 x=–2/3
3x-2=0 3x=–2 x=–2/3

4. 8x² – 6x = 2
8x²–6x–2=0
(4x+1)(2x–2)=0
4x+1=0 4x=–1 x=–1/4
2x–2=0 2x=2 x=1

5. 2x²+ 5x = 0

6. x² + 6x - 40 = 0

7.2x²+ 2x = 28

Multiply the binomials. use the FOIL method (First Inside Outside Last)

8. (x + 3)(x – 5)
1x²–5x+3x–15
1x²–2x–15

9. (3x – 5)(2x + 1)
=6x²+3x–10x–5
=6x²–7x–5

10. (x + 4)(x – 3)
=1x²–3x+4x–12
= 1x²+x–12

11. (x + 4)(x - 4)
=1x²–4x+4x–16
=1x²–16

12. (x – 5)( 2x + 5)
=2x²+5x-10x-25
= 2x²-5x-25

Answer 3

1. x(x – 3) = 0 [x = 0 , 3]

2. x2 + 3x + 2 = 0
(x+1)(x+2)= 0 so x = -1, -2

3.9x2 – 12x = -4
(3x^2 -2)^2 = 0 so x = +/- sqrt (2/3) = +/- sqrt(6)/3

4.8x2 – 6x = 2
(8x+2)(x-1) = 0, so x = -1/4 , 1

5. 2x2+ 5x = 0
x(2x+5) = 0, so x =0, -2.5

6. x2 + 6x - 40 = 0
(x+10)(x-4) = 0, so x = -10 , 4

7. 2x2 + 2x = 28
x^2+x-14=0
x = [-1 +/1sqrt(1-4(1)(-14)]/2
= [-1 +/- sqrt(57)]/2

(x + 3)(x – 5) = x^2 -2x -15
(3x – 5)(2x + 1) = 6x^2 -7x -5
(x + 4)(x – 3)= x^2+x-12
(x + 4)(x - 4)= x^2-16
(x – 5)( 2x + 5) = 2x^2 -5x -25

Answer 4

One elementary term that looks regularly is "equations." for many, this could be a buzz observe that's recognizable as a math term yet quite awareness the term could sometime escape people. the two maximum elementary equations are linear equations and quadratic equations yet, of course, purely giving an equation a acceptance does not unavoidably clarify what it relatively is. So, a clearer definition of what precisely the two maximum elementary equations - linear and quadratic equations - is mandatory. A linear equation refers to a particular equation that's graphed on a without delay line. additionally, a linear equation possesses on the line one variable that's regularly stated as "X" and "X" will constantly be of a level that's a million at maximum. (that's, there are actually not any exponents; yet once you're searching for exponents then wait and notice via fact we are able to get to them presently!) a elementary occasion of a linear equation could be 1x + 2 = 3. of course, x could equivalent a million in this actual occasion and it relatively is located out with the aid of purely utilising a sprint algebra on the equation to make certain X. 3 minus 2 equals a million. as a result, X could desire to equivalent one as a million x a million equals one. And, nope, no longer all linear equations are that effortless as they arrive as complicated as 6(x + 3) = 24 (x +0), however the elementary element of separating x to discover the answer does not substitute. A quadratic equation is in basic terms diverse from a linear equation in a single admire: various of of the figures is squared. (The observe quadratic derives from the Latin observe for squared) the elementary sort of a quadratic equation is ax2 + bx + c = 11. In this sort of equation, if a = a million, b = 2 and c = 3 then X could desire to equivalent 2. all of us recognize this via fact 2 squared is 4 and four x a million = 4. 2 x 2 = 4. As with a linear equation, there could be extra complicated variations of a quadratic equation yet in basic terms with the easy and complicated linear equations elementary algebraic operations can yield the main stunning answer.

Answer 5

1) x=o or x=3
2)x2+3x+2=0
.'.x2+2x+x+2=0
.'.x(x+2)+1(x+2)=0
.'.(x+1)(x+2)=0
.'.x= -1 or x= -2
3)9x2-12x=-4
.'.9x2-12x+4=0
.'.9x2-6x-6x+4=0
.'.3x(3x-2)-2(3x-2)=0
.'.(3x-2)(3x-2)=0
.'.x=2/3
4)8x2-6x=2
.'.8x2-6x-2=0
.'.8x2-8x+2x-2=0
.'.8x(x-1)+2(x-1)=0
.'.(8x+2)(x-1)=0
.'.x= -2/8= -1/4 or x=1

I will tell other questions later. SORRY.