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Simplifying x2 + -8x = 56 Reorder the terms: -8x + x2 = 56 Solving -8x + x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + -8x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -8x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -8x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -8x + x2 = 0 + 56 -8x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -8x + x2 = 56 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 = 56 + 16 Reorder the terms: 16 + -8x + x2 = 56 + 16 Combine like terms: 56 + 16 = 72 16 + -8x + x2 = 72 Factor a perfect square on the left side: (x + -4)(x + -4) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -4) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -4 = 8.485281374 Simplifying x + -4 = 8.485281374 Reorder the terms: -4 + x = 8.485281374 Solving -4 + x = 8.485281374 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 = 8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.485281374 + 4 x = 8.485281374 + 4 Combine like terms: 8.485281374 + 4 = 12.485281374 x = 12.485281374 Simplifying x = 12.485281374Subproblem 2
x + -4 = -8.485281374 Simplifying x + -4 = -8.485281374 Reorder the terms: -4 + x = -8.485281374 Solving -4 + x = -8.485281374 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 = -8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.485281374 + 4 x = -8.485281374 + 4 Combine like terms: -8.485281374 + 4 = -4.485281374 x = -4.485281374 Simplifying x = -4.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.485281374, -4.485281374}
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