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Simplifying x2 + -18x + -77 = 10 Reorder the terms: -77 + -18x + x2 = 10 Solving -77 + -18x + x2 = 10 Solving for variable 'x'. Reorder the terms: -77 + -10 + -18x + x2 = 10 + -10 Combine like terms: -77 + -10 = -87 -87 + -18x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -87 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + -18x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + -18x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + -18x + x2 = 0 + 87 -18x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 -18x + x2 = 87 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 87 + 81 Reorder the terms: 81 + -18x + x2 = 87 + 81 Combine like terms: 87 + 81 = 168 81 + -18x + x2 = 168 Factor a perfect square on the left side: (x + -9)(x + -9) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + -9) equal to 12.961481397 and -12.961481397.Subproblem 1
x + -9 = 12.961481397 Simplifying x + -9 = 12.961481397 Reorder the terms: -9 + x = 12.961481397 Solving -9 + x = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 12.961481397 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.961481397 + 9 x = 12.961481397 + 9 Combine like terms: 12.961481397 + 9 = 21.961481397 x = 21.961481397 Simplifying x = 21.961481397Subproblem 2
x + -9 = -12.961481397 Simplifying x + -9 = -12.961481397 Reorder the terms: -9 + x = -12.961481397 Solving -9 + x = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -12.961481397 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.961481397 + 9 x = -12.961481397 + 9 Combine like terms: -12.961481397 + 9 = -3.961481397 x = -3.961481397 Simplifying x = -3.961481397Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.961481397, -3.961481397}
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