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Simplifying 180 = x2 + 2x + -6 Reorder the terms: 180 = -6 + 2x + x2 Solving 180 = -6 + 2x + x2 Solving for variable 'x'. Combine like terms: 180 + 6 = 186 186 + -2x + -1x2 = -6 + 2x + x2 + 6 + -2x + -1x2 Reorder the terms: 186 + -2x + -1x2 = -6 + 6 + 2x + -2x + x2 + -1x2 Combine like terms: -6 + 6 = 0 186 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 186 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 186 + -2x + -1x2 = 0 + x2 + -1x2 186 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 186 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -186 + 2x + x2 = 0 Move the constant term to the right: Add '186' to each side of the equation. -186 + 2x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + 2x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 2x + x2 = 0 + 186 2x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 2x + x2 = 186 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 186 + 1 Reorder the terms: 1 + 2x + x2 = 186 + 1 Combine like terms: 186 + 1 = 187 1 + 2x + x2 = 187 Factor a perfect square on the left side: (x + 1)(x + 1) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (x + 1) equal to 13.674794331 and -13.674794331.Subproblem 1
x + 1 = 13.674794331 Simplifying x + 1 = 13.674794331 Reorder the terms: 1 + x = 13.674794331 Solving 1 + x = 13.674794331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.674794331 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.674794331 + -1 x = 13.674794331 + -1 Combine like terms: 13.674794331 + -1 = 12.674794331 x = 12.674794331 Simplifying x = 12.674794331Subproblem 2
x + 1 = -13.674794331 Simplifying x + 1 = -13.674794331 Reorder the terms: 1 + x = -13.674794331 Solving 1 + x = -13.674794331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.674794331 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.674794331 + -1 x = -13.674794331 + -1 Combine like terms: -13.674794331 + -1 = -14.674794331 x = -14.674794331 Simplifying x = -14.674794331Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.674794331, -14.674794331}
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