x=-2x^2+10

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


Simplifying
x = -2x2 + 10

Reorder the terms:
x = 10 + -2x2

Solving
x = 10 + -2x2

Solving for variable 'x'.

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

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

Combine like terms: 10 + -10 = 0
-10 + x + 2x2 = 0 + -2x2 + 2x2
-10 + x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-10 + x + 2x2 = 0

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

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-2.5, 2}

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