x^2-3x=9-x^2

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Solution for x^2-3x=9-x^2 equation:


Simplifying
x2 + -3x = 9 + -1x2

Reorder the terms:
-3x + x2 = 9 + -1x2

Solving
-3x + x2 = 9 + -1x2

Solving for variable 'x'.

Reorder the terms:
-9 + -3x + x2 + x2 = 9 + -1x2 + -9 + x2

Combine like terms: x2 + x2 = 2x2
-9 + -3x + 2x2 = 9 + -1x2 + -9 + x2

Reorder the terms:
-9 + -3x + 2x2 = 9 + -9 + -1x2 + x2

Combine like terms: 9 + -9 = 0
-9 + -3x + 2x2 = 0 + -1x2 + x2
-9 + -3x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-9 + -3x + 2x2 = 0

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

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

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

Solution

x = {-1.5, 3}

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