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Simplifying 4x2 + 61x = 5701 Reorder the terms: 61x + 4x2 = 5701 Solving 61x + 4x2 = 5701 Solving for variable 'x'. Reorder the terms: -5701 + 61x + 4x2 = 5701 + -5701 Combine like terms: 5701 + -5701 = 0 -5701 + 61x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1425.25 + 15.25x + x2 = 0 Move the constant term to the right: Add '1425.25' to each side of the equation. -1425.25 + 15.25x + 1425.25 + x2 = 0 + 1425.25 Reorder the terms: -1425.25 + 1425.25 + 15.25x + x2 = 0 + 1425.25 Combine like terms: -1425.25 + 1425.25 = 0.00 0.00 + 15.25x + x2 = 0 + 1425.25 15.25x + x2 = 0 + 1425.25 Combine like terms: 0 + 1425.25 = 1425.25 15.25x + x2 = 1425.25 The x term is 15.25x. Take half its coefficient (7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. 15.25x + 58.140625 + x2 = 1425.25 + 58.140625 Reorder the terms: 58.140625 + 15.25x + x2 = 1425.25 + 58.140625 Combine like terms: 1425.25 + 58.140625 = 1483.390625 58.140625 + 15.25x + x2 = 1483.390625 Factor a perfect square on the left side: (x + 7.625)(x + 7.625) = 1483.390625 Calculate the square root of the right side: 38.514810463 Break this problem into two subproblems by setting (x + 7.625) equal to 38.514810463 and -38.514810463.Subproblem 1
x + 7.625 = 38.514810463 Simplifying x + 7.625 = 38.514810463 Reorder the terms: 7.625 + x = 38.514810463 Solving 7.625 + x = 38.514810463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.625' to each side of the equation. 7.625 + -7.625 + x = 38.514810463 + -7.625 Combine like terms: 7.625 + -7.625 = 0.000 0.000 + x = 38.514810463 + -7.625 x = 38.514810463 + -7.625 Combine like terms: 38.514810463 + -7.625 = 30.889810463 x = 30.889810463 Simplifying x = 30.889810463Subproblem 2
x + 7.625 = -38.514810463 Simplifying x + 7.625 = -38.514810463 Reorder the terms: 7.625 + x = -38.514810463 Solving 7.625 + x = -38.514810463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.625' to each side of the equation. 7.625 + -7.625 + x = -38.514810463 + -7.625 Combine like terms: 7.625 + -7.625 = 0.000 0.000 + x = -38.514810463 + -7.625 x = -38.514810463 + -7.625 Combine like terms: -38.514810463 + -7.625 = -46.139810463 x = -46.139810463 Simplifying x = -46.139810463Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.889810463, -46.139810463}
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