5x^2+5=-5x^2+11x+11

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Solution for 5x^2+5=-5x^2+11x+11 equation:


Simplifying
5x2 + 5 = -5x2 + 11x + 11

Reorder the terms:
5 + 5x2 = -5x2 + 11x + 11

Reorder the terms:
5 + 5x2 = 11 + 11x + -5x2

Solving
5 + 5x2 = 11 + 11x + -5x2

Solving for variable 'x'.

Reorder the terms:
5 + -11 + -11x + 5x2 + 5x2 = 11 + 11x + -5x2 + -11 + -11x + 5x2

Combine like terms: 5 + -11 = -6
-6 + -11x + 5x2 + 5x2 = 11 + 11x + -5x2 + -11 + -11x + 5x2

Combine like terms: 5x2 + 5x2 = 10x2
-6 + -11x + 10x2 = 11 + 11x + -5x2 + -11 + -11x + 5x2

Reorder the terms:
-6 + -11x + 10x2 = 11 + -11 + 11x + -11x + -5x2 + 5x2

Combine like terms: 11 + -11 = 0
-6 + -11x + 10x2 = 0 + 11x + -11x + -5x2 + 5x2
-6 + -11x + 10x2 = 11x + -11x + -5x2 + 5x2

Combine like terms: 11x + -11x = 0
-6 + -11x + 10x2 = 0 + -5x2 + 5x2
-6 + -11x + 10x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-6 + -11x + 10x2 = 0

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

Subproblem 1

Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4

Subproblem 2

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {-0.4, 1.5}

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