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Simplifying 32 = 5x + x2 Solving 32 = 5x + x2 Solving for variable 'x'. Reorder the terms: 32 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 32 + -5x + -1x2 = 0 + x2 + -1x2 32 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 32 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -32 + 5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + 5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 5x + x2 = 0 + 32 5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 5x + x2 = 32 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 32 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 32 + 6.25 Combine like terms: 32 + 6.25 = 38.25 6.25 + 5x + x2 = 38.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 2.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 2.5 = 6.184658438 Simplifying x + 2.5 = 6.184658438 Reorder the terms: 2.5 + x = 6.184658438 Solving 2.5 + x = 6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.184658438 + -2.5 x = 6.184658438 + -2.5 Combine like terms: 6.184658438 + -2.5 = 3.684658438 x = 3.684658438 Simplifying x = 3.684658438Subproblem 2
x + 2.5 = -6.184658438 Simplifying x + 2.5 = -6.184658438 Reorder the terms: 2.5 + x = -6.184658438 Solving 2.5 + x = -6.184658438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.184658438 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.184658438 + -2.5 x = -6.184658438 + -2.5 Combine like terms: -6.184658438 + -2.5 = -8.684658438 x = -8.684658438 Simplifying x = -8.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.684658438, -8.684658438}
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