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Simplifying (15 + 6) * 6 = ((x + 1) + (x + -3)) * x + -3 Combine like terms: 15 + 6 = 21 (21) * 6 = ((x + 1) + (x + -3)) * x + -3 Multiply 21 * 6 126 = ((x + 1) + (x + -3)) * x + -3 Reorder the terms: 126 = ((1 + x) + (x + -3)) * x + -3 Remove parenthesis around (1 + x) 126 = (1 + x + (x + -3)) * x + -3 Reorder the terms: 126 = (1 + x + (-3 + x)) * x + -3 Remove parenthesis around (-3 + x) 126 = (1 + x + -3 + x) * x + -3 Reorder the terms: 126 = (1 + -3 + x + x) * x + -3 Combine like terms: 1 + -3 = -2 126 = (-2 + x + x) * x + -3 Combine like terms: x + x = 2x 126 = (-2 + 2x) * x + -3 Reorder the terms for easier multiplication: 126 = x(-2 + 2x) + -3 126 = (-2 * x + 2x * x) + -3 126 = (-2x + 2x2) + -3 Reorder the terms: 126 = -3 + -2x + 2x2 Solving 126 = -3 + -2x + 2x2 Solving for variable 'x'. Combine like terms: 126 + 3 = 129 129 + 2x + -2x2 = -3 + -2x + 2x2 + 3 + 2x + -2x2 Reorder the terms: 129 + 2x + -2x2 = -3 + 3 + -2x + 2x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 129 + 2x + -2x2 = 0 + -2x + 2x + 2x2 + -2x2 129 + 2x + -2x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 129 + 2x + -2x2 = 0 + 2x2 + -2x2 129 + 2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 129 + 2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -64.5 + -1x + x2 = 0 Move the constant term to the right: Add '64.5' to each side of the equation. -64.5 + -1x + 64.5 + x2 = 0 + 64.5 Reorder the terms: -64.5 + 64.5 + -1x + x2 = 0 + 64.5 Combine like terms: -64.5 + 64.5 = 0.0 0.0 + -1x + x2 = 0 + 64.5 -1x + x2 = 0 + 64.5 Combine like terms: 0 + 64.5 = 64.5 -1x + x2 = 64.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 64.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 64.5 + 0.25 Combine like terms: 64.5 + 0.25 = 64.75 0.25 + -1x + x2 = 64.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 64.75 Calculate the square root of the right side: 8.04673847 Break this problem into two subproblems by setting (x + -0.5) equal to 8.04673847 and -8.04673847.Subproblem 1
x + -0.5 = 8.04673847 Simplifying x + -0.5 = 8.04673847 Reorder the terms: -0.5 + x = 8.04673847 Solving -0.5 + x = 8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.04673847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.04673847 + 0.5 x = 8.04673847 + 0.5 Combine like terms: 8.04673847 + 0.5 = 8.54673847 x = 8.54673847 Simplifying x = 8.54673847Subproblem 2
x + -0.5 = -8.04673847 Simplifying x + -0.5 = -8.04673847 Reorder the terms: -0.5 + x = -8.04673847 Solving -0.5 + x = -8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.04673847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.04673847 + 0.5 x = -8.04673847 + 0.5 Combine like terms: -8.04673847 + 0.5 = -7.54673847 x = -7.54673847 Simplifying x = -7.54673847Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.54673847, -7.54673847}
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