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Simplifying x2 + -26x + 84.5 = 0 Reorder the terms: 84.5 + -26x + x2 = 0 Solving 84.5 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-84.5' to each side of the equation. 84.5 + -26x + -84.5 + x2 = 0 + -84.5 Reorder the terms: 84.5 + -84.5 + -26x + x2 = 0 + -84.5 Combine like terms: 84.5 + -84.5 = 0.0 0.0 + -26x + x2 = 0 + -84.5 -26x + x2 = 0 + -84.5 Combine like terms: 0 + -84.5 = -84.5 -26x + x2 = -84.5 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 = -84.5 + 169 Reorder the terms: 169 + -26x + x2 = -84.5 + 169 Combine like terms: -84.5 + 169 = 84.5 169 + -26x + x2 = 84.5 Factor a perfect square on the left side: (x + -13)(x + -13) = 84.5 Calculate the square root of the right side: 9.192388155 Break this problem into two subproblems by setting (x + -13) equal to 9.192388155 and -9.192388155.Subproblem 1
x + -13 = 9.192388155 Simplifying x + -13 = 9.192388155 Reorder the terms: -13 + x = 9.192388155 Solving -13 + x = 9.192388155 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 = 9.192388155 + 13 Combine like terms: -13 + 13 = 0 0 + x = 9.192388155 + 13 x = 9.192388155 + 13 Combine like terms: 9.192388155 + 13 = 22.192388155 x = 22.192388155 Simplifying x = 22.192388155Subproblem 2
x + -13 = -9.192388155 Simplifying x + -13 = -9.192388155 Reorder the terms: -13 + x = -9.192388155 Solving -13 + x = -9.192388155 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 = -9.192388155 + 13 Combine like terms: -13 + 13 = 0 0 + x = -9.192388155 + 13 x = -9.192388155 + 13 Combine like terms: -9.192388155 + 13 = 3.807611845 x = 3.807611845 Simplifying x = 3.807611845Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.192388155, 3.807611845}
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