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Simplifying 0.125x2 + -1x + -16 = 0 Reorder the terms: -16 + -1x + 0.125x2 = 0 Solving -16 + -1x + 0.125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. -128 + -8x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + -8x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -8x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -8x + x2 = 0 + 128 -8x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -8x + x2 = 128 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 = 128 + 16 Reorder the terms: 16 + -8x + x2 = 128 + 16 Combine like terms: 128 + 16 = 144 16 + -8x + x2 = 144 Factor a perfect square on the left side: (x + -4)(x + -4) = 144 Calculate the square root of the right side: 12 Break this problem into two subproblems by setting (x + -4) equal to 12 and -12.Subproblem 1
x + -4 = 12 Simplifying x + -4 = 12 Reorder the terms: -4 + x = 12 Solving -4 + x = 12 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 + 4 Combine like terms: -4 + 4 = 0 0 + x = 12 + 4 x = 12 + 4 Combine like terms: 12 + 4 = 16 x = 16 Simplifying x = 16Subproblem 2
x + -4 = -12 Simplifying x + -4 = -12 Reorder the terms: -4 + x = -12 Solving -4 + x = -12 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 + 4 Combine like terms: -4 + 4 = 0 0 + x = -12 + 4 x = -12 + 4 Combine like terms: -12 + 4 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, -8}
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