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Simplifying x2 + -52x + -8 = 0 Reorder the terms: -8 + -52x + x2 = 0 Solving -8 + -52x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -52x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -52x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -52x + x2 = 0 + 8 -52x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -52x + x2 = 8 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = 8 + 676 Reorder the terms: 676 + -52x + x2 = 8 + 676 Combine like terms: 8 + 676 = 684 676 + -52x + x2 = 684 Factor a perfect square on the left side: (x + -26)(x + -26) = 684 Calculate the square root of the right side: 26.153393661 Break this problem into two subproblems by setting (x + -26) equal to 26.153393661 and -26.153393661.Subproblem 1
x + -26 = 26.153393661 Simplifying x + -26 = 26.153393661 Reorder the terms: -26 + x = 26.153393661 Solving -26 + x = 26.153393661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 26.153393661 + 26 Combine like terms: -26 + 26 = 0 0 + x = 26.153393661 + 26 x = 26.153393661 + 26 Combine like terms: 26.153393661 + 26 = 52.153393661 x = 52.153393661 Simplifying x = 52.153393661Subproblem 2
x + -26 = -26.153393661 Simplifying x + -26 = -26.153393661 Reorder the terms: -26 + x = -26.153393661 Solving -26 + x = -26.153393661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -26.153393661 + 26 Combine like terms: -26 + 26 = 0 0 + x = -26.153393661 + 26 x = -26.153393661 + 26 Combine like terms: -26.153393661 + 26 = -0.153393661 x = -0.153393661 Simplifying x = -0.153393661Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.153393661, -0.153393661}
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