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Simplifying 0.625x2 + 5x = 57750 Reorder the terms: 5x + 0.625x2 = 57750 Solving 5x + 0.625x2 = 57750 Solving for variable 'x'. Reorder the terms: -57750 + 5x + 0.625x2 = 57750 + -57750 Combine like terms: 57750 + -57750 = 0 -57750 + 5x + 0.625x2 = 0 Begin completing the square. Divide all terms by 0.625 the coefficient of the squared term: Divide each side by '0.625'. -92400 + 8x + x2 = 0 Move the constant term to the right: Add '92400' to each side of the equation. -92400 + 8x + 92400 + x2 = 0 + 92400 Reorder the terms: -92400 + 92400 + 8x + x2 = 0 + 92400 Combine like terms: -92400 + 92400 = 0 0 + 8x + x2 = 0 + 92400 8x + x2 = 0 + 92400 Combine like terms: 0 + 92400 = 92400 8x + x2 = 92400 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 = 92400 + 16 Reorder the terms: 16 + 8x + x2 = 92400 + 16 Combine like terms: 92400 + 16 = 92416 16 + 8x + x2 = 92416 Factor a perfect square on the left side: (x + 4)(x + 4) = 92416 Calculate the square root of the right side: 304 Break this problem into two subproblems by setting (x + 4) equal to 304 and -304.Subproblem 1
x + 4 = 304 Simplifying x + 4 = 304 Reorder the terms: 4 + x = 304 Solving 4 + x = 304 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 = 304 + -4 Combine like terms: 4 + -4 = 0 0 + x = 304 + -4 x = 304 + -4 Combine like terms: 304 + -4 = 300 x = 300 Simplifying x = 300Subproblem 2
x + 4 = -304 Simplifying x + 4 = -304 Reorder the terms: 4 + x = -304 Solving 4 + x = -304 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 = -304 + -4 Combine like terms: 4 + -4 = 0 0 + x = -304 + -4 x = -304 + -4 Combine like terms: -304 + -4 = -308 x = -308 Simplifying x = -308Solution
The solution to the problem is based on the solutions from the subproblems. x = {300, -308}
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