Question

Solve, using the quadratic formula: 6x^2 = -5x + 25 (Points : 1)
{-5/3, 5/2}
{5/3, -5/2}
No real solutions

Answer 1

@miamia6547



Simplifying
6x2 = -5x + 25

Reorder the terms:
6x2 = 25 + -5x

Solving
6x2 = 25 + -5x

Solving for variable 'x'.

Reorder the terms:
-25 + 5x + 6x2 = 25 + -5x + -25 + 5x

Reorder the terms:
-25 + 5x + 6x2 = 25 + -25 + -5x + 5x

Combine like terms: 25 + -25 = 0
-25 + 5x + 6x2 = 0 + -5x + 5x
-25 + 5x + 6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-25 + 5x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(5 + -3x) = 0

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-2.5, 1.666666667}