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Simplifying x2 + -18x + -68 = 0 Reorder the terms: -68 + -18x + x2 = 0 Solving -68 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + -18x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -18x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -18x + x2 = 0 + 68 -18x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -18x + x2 = 68 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 = 68 + 81 Reorder the terms: 81 + -18x + x2 = 68 + 81 Combine like terms: 68 + 81 = 149 81 + -18x + x2 = 149 Factor a perfect square on the left side: (x + -9)(x + -9) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + -9) equal to 12.206555616 and -12.206555616.Subproblem 1
x + -9 = 12.206555616 Simplifying x + -9 = 12.206555616 Reorder the terms: -9 + x = 12.206555616 Solving -9 + x = 12.206555616 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 = 12.206555616 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.206555616 + 9 x = 12.206555616 + 9 Combine like terms: 12.206555616 + 9 = 21.206555616 x = 21.206555616 Simplifying x = 21.206555616Subproblem 2
x + -9 = -12.206555616 Simplifying x + -9 = -12.206555616 Reorder the terms: -9 + x = -12.206555616 Solving -9 + x = -12.206555616 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 = -12.206555616 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.206555616 + 9 x = -12.206555616 + 9 Combine like terms: -12.206555616 + 9 = -3.206555616 x = -3.206555616 Simplifying x = -3.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.206555616, -3.206555616}
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