How do you solve (x + 5) ( x - 3) = - 2( 2x + 7)?

2 Answers
May 7, 2017

x=color(red)(-3+2sqrt10),color(blue)(-3-2sqrt10

Explanation:

Solve:

(x+5)(x-3)=-2(2x+7)

Expand.

(x+5)(x-3)=-4x-14

FOIL.

x^2+2x-15=-4x-14

Add 4x to both sides.

x^2+6x-15=-14

Add 14 to both sides.

x^2+6x-1

x^2+6x-1 is a quadratic equation in standard form: ax^2+bx+c, where a=1, b=6, c=-1.

Use the quadratic formula to solve.

x=(-b+-sqrt(b^2-4ac))/(2a)

Substitute the given values into the formula.

x=(-6+-sqrt(6^2-4xx1xx-1))/(2xx1)

Simplify.

x=(-6+-sqrt(36+4))/2

x=(-6+-sqrt(40))/2

Prime decompose sqrt(40).

x=(-6+-sqrt(2xx2xx2xx5))/2

x=(-6+-sqrt(2^2xx2xx5))/2

x=(-6+-2sqrt10)/2

Simplify.

x=-3+-2sqrt10

Solutions for x.

x=color(red)(-3+2sqrt10),color(blue)(-3-2sqrt10

May 7, 2017

x~~6.48
x~~ -4.48

Explanation:

(x+5)(x-3)= -2(2x+7)
x^2-3x+5x-15=4x+14
x^ (2+√120 ) / 2 (2+√120 ) / 2 (2+√120 ) / 2 (2+√120 ) / 2 =4x+14+3x-5x+15 x^2=4x+3x-5x+14+15 x^2=2x+29 x^2-2x-29=0#

Apply this formula:
(-b ±√b^2- 4ac) / (2a)

a=1
b=-2
c=-29

[- (-2) ±√(-2)^2 - (4×1× -29) ] / (2×1)

[2±√4 - (-116) ] / 2

[2±√4+116 ] / 2

[ 2±√120 ] / 2

(2+√120 ) / 2 or (2-√120)/2

~~ (2+10.95) /2 ~~(2-10.95)/2

12.95/2 = 6.48 -8.95/2 = -4.48