7x=2x^2-9

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Solution for 7x=2x^2-9 equation:


Simplifying
7x = 2x2 + -9

Reorder the terms:
7x = -9 + 2x2

Solving
7x = -9 + 2x2

Solving for variable 'x'.

Reorder the terms:
9 + 7x + -2x2 = -9 + 2x2 + 9 + -2x2

Reorder the terms:
9 + 7x + -2x2 = -9 + 9 + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
9 + 7x + -2x2 = 0 + 2x2 + -2x2
9 + 7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
9 + 7x + -2x2 = 0

Factor a trinomial.
(9 + -2x)(1 + x) = 0

Subproblem 1

Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5

Subproblem 2

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

Solution

x = {4.5, -1}

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