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Simplifying x(x + -26) = -126 Reorder the terms: x(-26 + x) = -126 (-26 * x + x * x) = -126 (-26x + x2) = -126 Solving -26x + x2 = -126 Solving for variable 'x'. Reorder the terms: 126 + -26x + x2 = -126 + 126 Combine like terms: -126 + 126 = 0 126 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + -26x + -126 + x2 = 0 + -126 Reorder the terms: 126 + -126 + -26x + x2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -26x + x2 = 0 + -126 -26x + x2 = 0 + -126 Combine like terms: 0 + -126 = -126 -26x + x2 = -126 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 = -126 + 169 Reorder the terms: 169 + -26x + x2 = -126 + 169 Combine like terms: -126 + 169 = 43 169 + -26x + x2 = 43 Factor a perfect square on the left side: (x + -13)(x + -13) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -13) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -13 = 6.557438524 Simplifying x + -13 = 6.557438524 Reorder the terms: -13 + x = 6.557438524 Solving -13 + x = 6.557438524 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 = 6.557438524 + 13 Combine like terms: -13 + 13 = 0 0 + x = 6.557438524 + 13 x = 6.557438524 + 13 Combine like terms: 6.557438524 + 13 = 19.557438524 x = 19.557438524 Simplifying x = 19.557438524Subproblem 2
x + -13 = -6.557438524 Simplifying x + -13 = -6.557438524 Reorder the terms: -13 + x = -6.557438524 Solving -13 + x = -6.557438524 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 = -6.557438524 + 13 Combine like terms: -13 + 13 = 0 0 + x = -6.557438524 + 13 x = -6.557438524 + 13 Combine like terms: -6.557438524 + 13 = 6.442561476 x = 6.442561476 Simplifying x = 6.442561476Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.557438524, 6.442561476}
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