10=-2x^2+4x+8

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Solution for 10=-2x^2+4x+8 equation:


Simplifying
10 = -2x2 + 4x + 8

Reorder the terms:
10 = 8 + 4x + -2x2

Solving
10 = 8 + 4x + -2x2

Solving for variable 'x'.

Combine like terms: 10 + -8 = 2
2 + -4x + 2x2 = 8 + 4x + -2x2 + -8 + -4x + 2x2

Reorder the terms:
2 + -4x + 2x2 = 8 + -8 + 4x + -4x + -2x2 + 2x2

Combine like terms: 8 + -8 = 0
2 + -4x + 2x2 = 0 + 4x + -4x + -2x2 + 2x2
2 + -4x + 2x2 = 4x + -4x + -2x2 + 2x2

Combine like terms: 4x + -4x = 0
2 + -4x + 2x2 = 0 + -2x2 + 2x2
2 + -4x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
2 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2x + x2) = 0

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

Ignore the factor 2.

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 '(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

Solution

x = {1, 1}

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