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Simplifying x = -2x2 + 12x + 7 Reorder the terms: x = 7 + 12x + -2x2 Solving x = 7 + 12x + -2x2 Solving for variable 'x'. Reorder the terms: -7 + x + -12x + 2x2 = 7 + 12x + -2x2 + -7 + -12x + 2x2 Combine like terms: x + -12x = -11x -7 + -11x + 2x2 = 7 + 12x + -2x2 + -7 + -12x + 2x2 Reorder the terms: -7 + -11x + 2x2 = 7 + -7 + 12x + -12x + -2x2 + 2x2 Combine like terms: 7 + -7 = 0 -7 + -11x + 2x2 = 0 + 12x + -12x + -2x2 + 2x2 -7 + -11x + 2x2 = 12x + -12x + -2x2 + 2x2 Combine like terms: 12x + -12x = 0 -7 + -11x + 2x2 = 0 + -2x2 + 2x2 -7 + -11x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -7 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -5.5x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -5.5x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -5.5x + x2 = 0 + 3.5 -5.5x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -5.5x + x2 = 3.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 3.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 3.5 + 7.5625 Combine like terms: 3.5 + 7.5625 = 11.0625 7.5625 + -5.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -2.75) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -2.75 = 3.326033674 Simplifying x + -2.75 = 3.326033674 Reorder the terms: -2.75 + x = 3.326033674 Solving -2.75 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.326033674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.326033674 + 2.75 x = 3.326033674 + 2.75 Combine like terms: 3.326033674 + 2.75 = 6.076033674 x = 6.076033674 Simplifying x = 6.076033674Subproblem 2
x + -2.75 = -3.326033674 Simplifying x + -2.75 = -3.326033674 Reorder the terms: -2.75 + x = -3.326033674 Solving -2.75 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.326033674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.326033674 + 2.75 x = -3.326033674 + 2.75 Combine like terms: -3.326033674 + 2.75 = -0.576033674 x = -0.576033674 Simplifying x = -0.576033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.076033674, -0.576033674}
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