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Simplifying x2 + -26x + -7 = 9 Reorder the terms: -7 + -26x + x2 = 9 Solving -7 + -26x + x2 = 9 Solving for variable 'x'. Reorder the terms: -7 + -9 + -26x + x2 = 9 + -9 Combine like terms: -7 + -9 = -16 -16 + -26x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -16 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -26x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -26x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -26x + x2 = 0 + 16 -26x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -26x + x2 = 16 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 = 16 + 169 Reorder the terms: 169 + -26x + x2 = 16 + 169 Combine like terms: 16 + 169 = 185 169 + -26x + x2 = 185 Factor a perfect square on the left side: (x + -13)(x + -13) = 185 Calculate the square root of the right side: 13.601470509 Break this problem into two subproblems by setting (x + -13) equal to 13.601470509 and -13.601470509.Subproblem 1
x + -13 = 13.601470509 Simplifying x + -13 = 13.601470509 Reorder the terms: -13 + x = 13.601470509 Solving -13 + x = 13.601470509 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 = 13.601470509 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.601470509 + 13 x = 13.601470509 + 13 Combine like terms: 13.601470509 + 13 = 26.601470509 x = 26.601470509 Simplifying x = 26.601470509Subproblem 2
x + -13 = -13.601470509 Simplifying x + -13 = -13.601470509 Reorder the terms: -13 + x = -13.601470509 Solving -13 + x = -13.601470509 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 = -13.601470509 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.601470509 + 13 x = -13.601470509 + 13 Combine like terms: -13.601470509 + 13 = -0.601470509 x = -0.601470509 Simplifying x = -0.601470509Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.601470509, -0.601470509}
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