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Simplifying -26x + x2 = -152 Solving -26x + x2 = -152 Solving for variable 'x'. Reorder the terms: 152 + -26x + x2 = -152 + 152 Combine like terms: -152 + 152 = 0 152 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-152' to each side of the equation. 152 + -26x + -152 + x2 = 0 + -152 Reorder the terms: 152 + -152 + -26x + x2 = 0 + -152 Combine like terms: 152 + -152 = 0 0 + -26x + x2 = 0 + -152 -26x + x2 = 0 + -152 Combine like terms: 0 + -152 = -152 -26x + x2 = -152 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 = -152 + 169 Reorder the terms: 169 + -26x + x2 = -152 + 169 Combine like terms: -152 + 169 = 17 169 + -26x + x2 = 17 Factor a perfect square on the left side: (x + -13)(x + -13) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -13) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -13 = 4.123105626 Simplifying x + -13 = 4.123105626 Reorder the terms: -13 + x = 4.123105626 Solving -13 + x = 4.123105626 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 = 4.123105626 + 13 Combine like terms: -13 + 13 = 0 0 + x = 4.123105626 + 13 x = 4.123105626 + 13 Combine like terms: 4.123105626 + 13 = 17.123105626 x = 17.123105626 Simplifying x = 17.123105626Subproblem 2
x + -13 = -4.123105626 Simplifying x + -13 = -4.123105626 Reorder the terms: -13 + x = -4.123105626 Solving -13 + x = -4.123105626 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 = -4.123105626 + 13 Combine like terms: -13 + 13 = 0 0 + x = -4.123105626 + 13 x = -4.123105626 + 13 Combine like terms: -4.123105626 + 13 = 8.876894374 x = 8.876894374 Simplifying x = 8.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.123105626, 8.876894374}
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