5x=2x^2-3

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


Simplifying
5x = 2x2 + -3

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

Solving
5x = -3 + 2x2

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(3 + -1x)(1 + 2x) = 0

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

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

Solution

x = {3, -0.5}

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