25=-2x^2+3x+27

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Solution for 25=-2x^2+3x+27 equation:


Simplifying
25 = -2x2 + 3x + 27

Reorder the terms:
25 = 27 + 3x + -2x2

Solving
25 = 27 + 3x + -2x2

Solving for variable 'x'.

Combine like terms: 25 + -27 = -2
-2 + -3x + 2x2 = 27 + 3x + -2x2 + -27 + -3x + 2x2

Reorder the terms:
-2 + -3x + 2x2 = 27 + -27 + 3x + -3x + -2x2 + 2x2

Combine like terms: 27 + -27 = 0
-2 + -3x + 2x2 = 0 + 3x + -3x + -2x2 + 2x2
-2 + -3x + 2x2 = 3x + -3x + -2x2 + 2x2

Combine like terms: 3x + -3x = 0
-2 + -3x + 2x2 = 0 + -2x2 + 2x2
-2 + -3x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2 + -3x + 2x2 = 0

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

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

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 = {-0.5, 2}

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