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Simplifying x2 + -8x + -132 = 0 Reorder the terms: -132 + -8x + x2 = 0 Solving -132 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '132' to each side of the equation. -132 + -8x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + -8x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + -8x + x2 = 0 + 132 -8x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 -8x + x2 = 132 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 132 + 16 Reorder the terms: 16 + -8x + x2 = 132 + 16 Combine like terms: 132 + 16 = 148 16 + -8x + x2 = 148 Factor a perfect square on the left side: (x + -4)(x + -4) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + -4) equal to 12.165525061 and -12.165525061.Subproblem 1
x + -4 = 12.165525061 Simplifying x + -4 = 12.165525061 Reorder the terms: -4 + x = 12.165525061 Solving -4 + x = 12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 12.165525061 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12.165525061 + 4 x = 12.165525061 + 4 Combine like terms: 12.165525061 + 4 = 16.165525061 x = 16.165525061 Simplifying x = 16.165525061Subproblem 2
x + -4 = -12.165525061 Simplifying x + -4 = -12.165525061 Reorder the terms: -4 + x = -12.165525061 Solving -4 + x = -12.165525061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -12.165525061 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12.165525061 + 4 x = -12.165525061 + 4 Combine like terms: -12.165525061 + 4 = -8.165525061 x = -8.165525061 Simplifying x = -8.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.165525061, -8.165525061}
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