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Simplifying x2 + -8x + -52 = 0 Reorder the terms: -52 + -8x + x2 = 0 Solving -52 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -8x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -8x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -8x + x2 = 0 + 52 -8x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -8x + x2 = 52 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 52 + 16 Reorder the terms: 16 + -8x + x2 = 52 + 16 Combine like terms: 52 + 16 = 68 16 + -8x + x2 = 68 Factor a perfect square on the left side: (x + -4)(x + -4) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -4) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -4 = 8.246211251 Simplifying x + -4 = 8.246211251 Reorder the terms: -4 + x = 8.246211251 Solving -4 + x = 8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.246211251 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.246211251 + 4 x = 8.246211251 + 4 Combine like terms: 8.246211251 + 4 = 12.246211251 x = 12.246211251 Simplifying x = 12.246211251Subproblem 2
x + -4 = -8.246211251 Simplifying x + -4 = -8.246211251 Reorder the terms: -4 + x = -8.246211251 Solving -4 + x = -8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.246211251 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.246211251 + 4 x = -8.246211251 + 4 Combine like terms: -8.246211251 + 4 = -4.246211251 x = -4.246211251 Simplifying x = -4.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.246211251, -4.246211251}
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