2x^2-12x+18=362

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Solution for 2x^2-12x+18=362 equation:


Simplifying
2x2 + -12x + 18 = 362

Reorder the terms:
18 + -12x + 2x2 = 362

Solving
18 + -12x + 2x2 = 362

Solving for variable 'x'.

Reorder the terms:
18 + -362 + -12x + 2x2 = 362 + -362

Combine like terms: 18 + -362 = -344
-344 + -12x + 2x2 = 362 + -362

Combine like terms: 362 + -362 = 0
-344 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-172 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-172 + -6x + x2)' equal to zero and attempt to solve: Simplifying -172 + -6x + x2 = 0 Solving -172 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + -6x + 172 + x2 = 0 + 172 Reorder the terms: -172 + 172 + -6x + x2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + -6x + x2 = 0 + 172 -6x + x2 = 0 + 172 Combine like terms: 0 + 172 = 172 -6x + x2 = 172 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 172 + 9 Reorder the terms: 9 + -6x + x2 = 172 + 9 Combine like terms: 172 + 9 = 181 9 + -6x + x2 = 181 Factor a perfect square on the left side: (x + -3)(x + -3) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + -3) equal to 13.453624047 and -13.453624047.

Subproblem 1

x + -3 = 13.453624047 Simplifying x + -3 = 13.453624047 Reorder the terms: -3 + x = 13.453624047 Solving -3 + x = 13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 13.453624047 + 3 Combine like terms: -3 + 3 = 0 0 + x = 13.453624047 + 3 x = 13.453624047 + 3 Combine like terms: 13.453624047 + 3 = 16.453624047 x = 16.453624047 Simplifying x = 16.453624047

Subproblem 2

x + -3 = -13.453624047 Simplifying x + -3 = -13.453624047 Reorder the terms: -3 + x = -13.453624047 Solving -3 + x = -13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -13.453624047 + 3 Combine like terms: -3 + 3 = 0 0 + x = -13.453624047 + 3 x = -13.453624047 + 3 Combine like terms: -13.453624047 + 3 = -10.453624047 x = -10.453624047 Simplifying x = -10.453624047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.453624047, -10.453624047}

Solution

x = {16.453624047, -10.453624047}

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