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Simplifying x2 + -26x = -9 Reorder the terms: -26x + x2 = -9 Solving -26x + x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + -26x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -26x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -26x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -26x + x2 = 0 + -9 -26x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -26x + x2 = -9 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 = -9 + 169 Reorder the terms: 169 + -26x + x2 = -9 + 169 Combine like terms: -9 + 169 = 160 169 + -26x + x2 = 160 Factor a perfect square on the left side: (x + -13)(x + -13) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -13) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -13 = 12.649110641 Simplifying x + -13 = 12.649110641 Reorder the terms: -13 + x = 12.649110641 Solving -13 + x = 12.649110641 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 = 12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.649110641 + 13 x = 12.649110641 + 13 Combine like terms: 12.649110641 + 13 = 25.649110641 x = 25.649110641 Simplifying x = 25.649110641Subproblem 2
x + -13 = -12.649110641 Simplifying x + -13 = -12.649110641 Reorder the terms: -13 + x = -12.649110641 Solving -13 + x = -12.649110641 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 = -12.649110641 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.649110641 + 13 x = -12.649110641 + 13 Combine like terms: -12.649110641 + 13 = 0.350889359 x = 0.350889359 Simplifying x = 0.350889359Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.649110641, 0.350889359}
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