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Simplifying (x + 6)(x) = 178 Reorder the terms: (6 + x)(x) = 178 Reorder the terms for easier multiplication: x(6 + x) = 178 (6 * x + x * x) = 178 (6x + x2) = 178 Solving 6x + x2 = 178 Solving for variable 'x'. Reorder the terms: -178 + 6x + x2 = 178 + -178 Combine like terms: 178 + -178 = 0 -178 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '178' to each side of the equation. -178 + 6x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 6x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 6x + x2 = 0 + 178 6x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 6x + x2 = 178 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 178 + 9 Reorder the terms: 9 + 6x + x2 = 178 + 9 Combine like terms: 178 + 9 = 187 9 + 6x + x2 = 187 Factor a perfect square on the left side: (x + 3)(x + 3) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (x + 3) equal to 13.674794331 and -13.674794331.Subproblem 1
x + 3 = 13.674794331 Simplifying x + 3 = 13.674794331 Reorder the terms: 3 + x = 13.674794331 Solving 3 + x = 13.674794331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.674794331 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.674794331 + -3 x = 13.674794331 + -3 Combine like terms: 13.674794331 + -3 = 10.674794331 x = 10.674794331 Simplifying x = 10.674794331Subproblem 2
x + 3 = -13.674794331 Simplifying x + 3 = -13.674794331 Reorder the terms: 3 + x = -13.674794331 Solving 3 + x = -13.674794331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.674794331 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.674794331 + -3 x = -13.674794331 + -3 Combine like terms: -13.674794331 + -3 = -16.674794331 x = -16.674794331 Simplifying x = -16.674794331Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.674794331, -16.674794331}
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