4x^2=10x+126

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Solution for 4x^2=10x+126 equation:


Simplifying
4x2 = 10x + 126

Reorder the terms:
4x2 = 126 + 10x

Solving
4x2 = 126 + 10x

Solving for variable 'x'.

Reorder the terms:
-126 + -10x + 4x2 = 126 + 10x + -126 + -10x

Reorder the terms:
-126 + -10x + 4x2 = 126 + -126 + 10x + -10x

Combine like terms: 126 + -126 = 0
-126 + -10x + 4x2 = 0 + 10x + -10x
-126 + -10x + 4x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-126 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-63 + -5x + 2x2) = 0

Factor a trinomial.
2((-9 + -2x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-4.5, 7}

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