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Simplifying x2 + -26x + 18 = 0 Reorder the terms: 18 + -26x + x2 = 0 Solving 18 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -26x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -26x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -26x + x2 = 0 + -18 -26x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -26x + x2 = -18 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -18 + 169 Reorder the terms: 169 + -26x + x2 = -18 + 169 Combine like terms: -18 + 169 = 151 169 + -26x + x2 = 151 Factor a perfect square on the left side: (x + -13)(x + -13) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + -13) equal to 12.288205727 and -12.288205727.Subproblem 1
x + -13 = 12.288205727 Simplifying x + -13 = 12.288205727 Reorder the terms: -13 + x = 12.288205727 Solving -13 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.288205727 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.288205727 + 13 x = 12.288205727 + 13 Combine like terms: 12.288205727 + 13 = 25.288205727 x = 25.288205727 Simplifying x = 25.288205727Subproblem 2
x + -13 = -12.288205727 Simplifying x + -13 = -12.288205727 Reorder the terms: -13 + x = -12.288205727 Solving -13 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.288205727 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.288205727 + 13 x = -12.288205727 + 13 Combine like terms: -12.288205727 + 13 = 0.711794273 x = 0.711794273 Simplifying x = 0.711794273Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.288205727, 0.711794273}
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