4x^2+1=-4x+36

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Solution for 4x^2+1=-4x+36 equation: 


Simplifying
4x2 + 1 = -4x + 36

Reorder the terms:
1 + 4x2 = -4x + 36

Reorder the terms:
1 + 4x2 = 36 + -4x

Solving
1 + 4x2 = 36 + -4x

Solving for variable 'x'.

Reorder the terms:
1 + -36 + 4x + 4x2 = 36 + -4x + -36 + 4x

Combine like terms: 1 + -36 = -35
-35 + 4x + 4x2 = 36 + -4x + -36 + 4x

Reorder the terms:
-35 + 4x + 4x2 = 36 + -36 + -4x + 4x

Combine like terms: 36 + -36 = 0
-35 + 4x + 4x2 = 0 + -4x + 4x
-35 + 4x + 4x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-35 + 4x + 4x2 = 0

Factor a trinomial.
(-7 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
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
Solution
x = {-3.5, 2.5}

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