Question

Find the roots of the equation x^2 = 30 -13x

Answer 1

Simplifying
x2 = 30 + -13x

Solving
x2 = 30 + -13x

Solving for variable 'x'.

Reorder the terms:
-30 + 13x + x2 = 30 + -13x + -30 + 13x

Reorder the terms:
-30 + 13x + x2 = 30 + -30 + -13x + 13x

Combine like terms: 30 + -30 = 0
-30 + 13x + x2 = 0 + -13x + 13x
-30 + 13x + x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-30 + 13x + x2 = 0

Factor a trinomial.
(-15 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-15, 2}

Answer 2

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Answer 3

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