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Simplifying -2x(x + -1) = x + -12 Reorder the terms: -2x(-1 + x) = x + -12 (-1 * -2x + x * -2x) = x + -12 (2x + -2x2) = x + -12 Reorder the terms: 2x + -2x2 = -12 + x Solving 2x + -2x2 = -12 + x Solving for variable 'x'. Reorder the terms: 12 + 2x + -1x + -2x2 = -12 + x + 12 + -1x Combine like terms: 2x + -1x = 1x 12 + 1x + -2x2 = -12 + x + 12 + -1x Reorder the terms: 12 + 1x + -2x2 = -12 + 12 + x + -1x Combine like terms: -12 + 12 = 0 12 + 1x + -2x2 = 0 + x + -1x 12 + 1x + -2x2 = x + -1x Combine like terms: x + -1x = 0 12 + 1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -0.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5x + x2 = 0 + 6 -0.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5x + x2 = 6 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 6 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 6 + 0.0625 Combine like terms: 6 + 0.0625 = 6.0625 0.0625 + -0.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -0.25) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -0.25 = 2.46221445 Simplifying x + -0.25 = 2.46221445 Reorder the terms: -0.25 + x = 2.46221445 Solving -0.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.46221445 + 0.25 x = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 x = 2.71221445 Simplifying x = 2.71221445Subproblem 2
x + -0.25 = -2.46221445 Simplifying x + -0.25 = -2.46221445 Reorder the terms: -0.25 + x = -2.46221445 Solving -0.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.46221445 + 0.25 x = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 x = -2.21221445 Simplifying x = -2.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.71221445, -2.21221445}
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