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Simplifying x2 + -13x + 40 = 5x Reorder the terms: 40 + -13x + x2 = 5x Solving 40 + -13x + x2 = 5x Solving for variable 'x'. Reorder the terms: 40 + -13x + -5x + x2 = 5x + -5x Combine like terms: -13x + -5x = -18x 40 + -18x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 40 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -18x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -18x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -18x + x2 = 0 + -40 -18x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -18x + x2 = -40 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 = -40 + 81 Reorder the terms: 81 + -18x + x2 = -40 + 81 Combine like terms: -40 + 81 = 41 81 + -18x + x2 = 41 Factor a perfect square on the left side: (x + -9)(x + -9) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -9) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -9 = 6.403124237 Simplifying x + -9 = 6.403124237 Reorder the terms: -9 + x = 6.403124237 Solving -9 + x = 6.403124237 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 = 6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x = 6.403124237 + 9 x = 6.403124237 + 9 Combine like terms: 6.403124237 + 9 = 15.403124237 x = 15.403124237 Simplifying x = 15.403124237Subproblem 2
x + -9 = -6.403124237 Simplifying x + -9 = -6.403124237 Reorder the terms: -9 + x = -6.403124237 Solving -9 + x = -6.403124237 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 = -6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x = -6.403124237 + 9 x = -6.403124237 + 9 Combine like terms: -6.403124237 + 9 = 2.596875763 x = 2.596875763 Simplifying x = 2.596875763Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.403124237, 2.596875763}
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