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Simplifying 560 = 32x + x2 Solving 560 = 32x + x2 Solving for variable 'x'. Reorder the terms: 560 + -32x + -1x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 560 + -32x + -1x2 = 0 + x2 + -1x2 560 + -32x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 560 + -32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -560 + 32x + x2 = 0 Move the constant term to the right: Add '560' to each side of the equation. -560 + 32x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + 32x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + 32x + x2 = 0 + 560 32x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 32x + x2 = 560 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 560 + 256 Reorder the terms: 256 + 32x + x2 = 560 + 256 Combine like terms: 560 + 256 = 816 256 + 32x + x2 = 816 Factor a perfect square on the left side: (x + 16)(x + 16) = 816 Calculate the square root of the right side: 28.565713714 Break this problem into two subproblems by setting (x + 16) equal to 28.565713714 and -28.565713714.Subproblem 1
x + 16 = 28.565713714 Simplifying x + 16 = 28.565713714 Reorder the terms: 16 + x = 28.565713714 Solving 16 + x = 28.565713714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 28.565713714 + -16 Combine like terms: 16 + -16 = 0 0 + x = 28.565713714 + -16 x = 28.565713714 + -16 Combine like terms: 28.565713714 + -16 = 12.565713714 x = 12.565713714 Simplifying x = 12.565713714Subproblem 2
x + 16 = -28.565713714 Simplifying x + 16 = -28.565713714 Reorder the terms: 16 + x = -28.565713714 Solving 16 + x = -28.565713714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -28.565713714 + -16 Combine like terms: 16 + -16 = 0 0 + x = -28.565713714 + -16 x = -28.565713714 + -16 Combine like terms: -28.565713714 + -16 = -44.565713714 x = -44.565713714 Simplifying x = -44.565713714Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.565713714, -44.565713714}
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