7x^2=-49+56x

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Solution for 7x^2=-49+56x equation:


Simplifying
7x2 = -49 + 56x

Solving
7x2 = -49 + 56x

Solving for variable 'x'.

Reorder the terms:
49 + -56x + 7x2 = -49 + 56x + 49 + -56x

Reorder the terms:
49 + -56x + 7x2 = -49 + 49 + 56x + -56x

Combine like terms: -49 + 49 = 0
49 + -56x + 7x2 = 0 + 56x + -56x
49 + -56x + 7x2 = 56x + -56x

Combine like terms: 56x + -56x = 0
49 + -56x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(7 + -8x + x2) = 0

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

Ignore the factor 7.

Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

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 = {1, 7}

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