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Simplifying x2 + -26x + 95 = 0 Reorder the terms: 95 + -26x + x2 = 0 Solving 95 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-95' to each side of the equation. 95 + -26x + -95 + x2 = 0 + -95 Reorder the terms: 95 + -95 + -26x + x2 = 0 + -95 Combine like terms: 95 + -95 = 0 0 + -26x + x2 = 0 + -95 -26x + x2 = 0 + -95 Combine like terms: 0 + -95 = -95 -26x + x2 = -95 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 = -95 + 169 Reorder the terms: 169 + -26x + x2 = -95 + 169 Combine like terms: -95 + 169 = 74 169 + -26x + x2 = 74 Factor a perfect square on the left side: (x + -13)(x + -13) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -13) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -13 = 8.602325267 Simplifying x + -13 = 8.602325267 Reorder the terms: -13 + x = 8.602325267 Solving -13 + x = 8.602325267 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 = 8.602325267 + 13 Combine like terms: -13 + 13 = 0 0 + x = 8.602325267 + 13 x = 8.602325267 + 13 Combine like terms: 8.602325267 + 13 = 21.602325267 x = 21.602325267 Simplifying x = 21.602325267Subproblem 2
x + -13 = -8.602325267 Simplifying x + -13 = -8.602325267 Reorder the terms: -13 + x = -8.602325267 Solving -13 + x = -8.602325267 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 = -8.602325267 + 13 Combine like terms: -13 + 13 = 0 0 + x = -8.602325267 + 13 x = -8.602325267 + 13 Combine like terms: -8.602325267 + 13 = 4.397674733 x = 4.397674733 Simplifying x = 4.397674733Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.602325267, 4.397674733}
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