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Simplifying x2 + -26x = -33 Reorder the terms: -26x + x2 = -33 Solving -26x + x2 = -33 Solving for variable 'x'. Reorder the terms: 33 + -26x + x2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + -26x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + -26x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -26x + x2 = 0 + -33 -26x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 -26x + x2 = -33 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 = -33 + 169 Reorder the terms: 169 + -26x + x2 = -33 + 169 Combine like terms: -33 + 169 = 136 169 + -26x + x2 = 136 Factor a perfect square on the left side: (x + -13)(x + -13) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + -13) equal to 11.66190379 and -11.66190379.Subproblem 1
x + -13 = 11.66190379 Simplifying x + -13 = 11.66190379 Reorder the terms: -13 + x = 11.66190379 Solving -13 + x = 11.66190379 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 = 11.66190379 + 13 Combine like terms: -13 + 13 = 0 0 + x = 11.66190379 + 13 x = 11.66190379 + 13 Combine like terms: 11.66190379 + 13 = 24.66190379 x = 24.66190379 Simplifying x = 24.66190379Subproblem 2
x + -13 = -11.66190379 Simplifying x + -13 = -11.66190379 Reorder the terms: -13 + x = -11.66190379 Solving -13 + x = -11.66190379 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 = -11.66190379 + 13 Combine like terms: -13 + 13 = 0 0 + x = -11.66190379 + 13 x = -11.66190379 + 13 Combine like terms: -11.66190379 + 13 = 1.33809621 x = 1.33809621 Simplifying x = 1.33809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.66190379, 1.33809621}
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