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Simplifying x2 + 18x + -59 = 0 Reorder the terms: -59 + 18x + x2 = 0 Solving -59 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 18x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + 18x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 18x + x2 = 0 + 59 18x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 18x + x2 = 59 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 = 59 + 81 Reorder the terms: 81 + 18x + x2 = 59 + 81 Combine like terms: 59 + 81 = 140 81 + 18x + x2 = 140 Factor a perfect square on the left side: (x + 9)(x + 9) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + 9) equal to 11.832159566 and -11.832159566.Subproblem 1
x + 9 = 11.832159566 Simplifying x + 9 = 11.832159566 Reorder the terms: 9 + x = 11.832159566 Solving 9 + x = 11.832159566 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 = 11.832159566 + -9 Combine like terms: 9 + -9 = 0 0 + x = 11.832159566 + -9 x = 11.832159566 + -9 Combine like terms: 11.832159566 + -9 = 2.832159566 x = 2.832159566 Simplifying x = 2.832159566Subproblem 2
x + 9 = -11.832159566 Simplifying x + 9 = -11.832159566 Reorder the terms: 9 + x = -11.832159566 Solving 9 + x = -11.832159566 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 = -11.832159566 + -9 Combine like terms: 9 + -9 = 0 0 + x = -11.832159566 + -9 x = -11.832159566 + -9 Combine like terms: -11.832159566 + -9 = -20.832159566 x = -20.832159566 Simplifying x = -20.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.832159566, -20.832159566}
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