8x^2+14x=15?

Question

statement says to solve....i missed that class lol

Answer 1

8x² + 14x = 15

Transpose 15

8x² + 14x - 15 = 15 - 15

8x² + 14x - 15 = 0

The middle term is + 14

Find the sum of the middle term

Multiply the first term 8 times the last term 15 equals 120 and factor

Factors of 120

1 x 120
2 x 60
3 x 40
4 x 30
5 x 24
6 x 20. . .←. .use these factors
8 x 15
10 x 12

- 6 and + 20 satisfy the sum of the middle term

insert - 6x + 20x into the equation

8x² + 14x - 15 = 0

8x² - 6x + 20x - 15 = 0

Group factor

(8x² - 6x) + (20x - 15) = 0

2x(4x - 3) + 5((4x - 3) = 0

(2x + 5)(4x - 3) = 0

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Roots

2x + 5 = 0

Transpose 5

2x + 5 - 5 = 0 - 5

2x = - 5

Divide both sides of the equation by 2

2x / 2 = - 5 / 2

x = - 5 / 2

x = 2 1/2

x = 2.5

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Roots

4x - 3 = 0

Transpose 3

4x - 3 + 3 0 + 3

4x = 3

Divide both sides of the equation by 4

4x/4 = 3/4

x = 3/4

- - - - - - -s-

Answer 2

8x^2 +14x = 15
=> 8x^2 + 14x - 15 = 0
=> (2x+5)(4x - 3) = 0

Hence, 2x + 5 = 0 or 4x - 3 = 0

2x + 5 = 0, x = -5/2

4x - 3 = 0, x = 3/4

Answer 3

8x^2 + 14x = 15
8x^2 + 14x - 15 = 0
quadratic formula
a=8
b=14
c=-15
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
x = (-14 +/- sqrt(196 + 480))/16
x= (-14 +/- 26)/16
x= -2.5 and x=+0.75 are the 2 solutions.