2x^2=24x-70

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Solution for 2x^2=24x-70 equation:


Simplifying
2x2 = 24x + -70

Reorder the terms:
2x2 = -70 + 24x

Solving
2x2 = -70 + 24x

Solving for variable 'x'.

Reorder the terms:
70 + -24x + 2x2 = -70 + 24x + 70 + -24x

Reorder the terms:
70 + -24x + 2x2 = -70 + 70 + 24x + -24x

Combine like terms: -70 + 70 = 0
70 + -24x + 2x2 = 0 + 24x + -24x
70 + -24x + 2x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
70 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -12x + x2) = 0

Factor a trinomial.
2((5 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 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 = {5, 7}

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