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Simplifying x + 49 = (x + -8)(x + -8) Reorder the terms: 49 + x = (x + -8)(x + -8) Reorder the terms: 49 + x = (-8 + x)(x + -8) Reorder the terms: 49 + x = (-8 + x)(-8 + x) Multiply (-8 + x) * (-8 + x) 49 + x = (-8(-8 + x) + x(-8 + x)) 49 + x = ((-8 * -8 + x * -8) + x(-8 + x)) 49 + x = ((64 + -8x) + x(-8 + x)) 49 + x = (64 + -8x + (-8 * x + x * x)) 49 + x = (64 + -8x + (-8x + x2)) Combine like terms: -8x + -8x = -16x 49 + x = (64 + -16x + x2) Solving 49 + x = 64 + -16x + x2 Solving for variable 'x'. Reorder the terms: 49 + -64 + x + 16x + -1x2 = 64 + -16x + x2 + -64 + 16x + -1x2 Combine like terms: 49 + -64 = -15 -15 + x + 16x + -1x2 = 64 + -16x + x2 + -64 + 16x + -1x2 Combine like terms: x + 16x = 17x -15 + 17x + -1x2 = 64 + -16x + x2 + -64 + 16x + -1x2 Reorder the terms: -15 + 17x + -1x2 = 64 + -64 + -16x + 16x + x2 + -1x2 Combine like terms: 64 + -64 = 0 -15 + 17x + -1x2 = 0 + -16x + 16x + x2 + -1x2 -15 + 17x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 -15 + 17x + -1x2 = 0 + x2 + -1x2 -15 + 17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15 + -17x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -17x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -17x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -17x + x2 = 0 + -15 -17x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -17x + x2 = -15 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -15 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -15 + 72.25 Combine like terms: -15 + 72.25 = 57.25 72.25 + -17x + x2 = 57.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + -8.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + -8.5 = 7.566372975 Simplifying x + -8.5 = 7.566372975 Reorder the terms: -8.5 + x = 7.566372975 Solving -8.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 7.566372975 + 8.5 x = 7.566372975 + 8.5 Combine like terms: 7.566372975 + 8.5 = 16.066372975 x = 16.066372975 Simplifying x = 16.066372975Subproblem 2
x + -8.5 = -7.566372975 Simplifying x + -8.5 = -7.566372975 Reorder the terms: -8.5 + x = -7.566372975 Solving -8.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -7.566372975 + 8.5 x = -7.566372975 + 8.5 Combine like terms: -7.566372975 + 8.5 = 0.933627025 x = 0.933627025 Simplifying x = 0.933627025Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.066372975, 0.933627025}
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