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Simplifying x = 2x2 + 8x + -16 Reorder the terms: x = -16 + 8x + 2x2 Solving x = -16 + 8x + 2x2 Solving for variable 'x'. Reorder the terms: 16 + x + -8x + -2x2 = -16 + 8x + 2x2 + 16 + -8x + -2x2 Combine like terms: x + -8x = -7x 16 + -7x + -2x2 = -16 + 8x + 2x2 + 16 + -8x + -2x2 Reorder the terms: 16 + -7x + -2x2 = -16 + 16 + 8x + -8x + 2x2 + -2x2 Combine like terms: -16 + 16 = 0 16 + -7x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2 16 + -7x + -2x2 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 16 + -7x + -2x2 = 0 + 2x2 + -2x2 16 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 16 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8 + 3.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 3.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 3.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3.5x + x2 = 0 + 8 3.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3.5x + x2 = 8 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 8 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 8 + 3.0625 Combine like terms: 8 + 3.0625 = 11.0625 3.0625 + 3.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 1.75) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 1.75 = 3.326033674 Simplifying x + 1.75 = 3.326033674 Reorder the terms: 1.75 + x = 3.326033674 Solving 1.75 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.326033674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.326033674 + -1.75 x = 3.326033674 + -1.75 Combine like terms: 3.326033674 + -1.75 = 1.576033674 x = 1.576033674 Simplifying x = 1.576033674Subproblem 2
x + 1.75 = -3.326033674 Simplifying x + 1.75 = -3.326033674 Reorder the terms: 1.75 + x = -3.326033674 Solving 1.75 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.326033674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.326033674 + -1.75 x = -3.326033674 + -1.75 Combine like terms: -3.326033674 + -1.75 = -5.076033674 x = -5.076033674 Simplifying x = -5.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.576033674, -5.076033674}
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