5x^2=-2x+3

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Solution for 5x^2=-2x+3 equation:


Simplifying
5x2 = -2x + 3

Reorder the terms:
5x2 = 3 + -2x

Solving
5x2 = 3 + -2x

Solving for variable 'x'.

Reorder the terms:
-3 + 2x + 5x2 = 3 + -2x + -3 + 2x

Reorder the terms:
-3 + 2x + 5x2 = 3 + -3 + -2x + 2x

Combine like terms: 3 + -3 = 0
-3 + 2x + 5x2 = 0 + -2x + 2x
-3 + 2x + 5x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-3 + 2x + 5x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -5x) = 0

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 '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Solution

x = {-1, 0.6}

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