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Simplifying 4x2 + 5x + -251 = 0 Reorder the terms: -251 + 5x + 4x2 = 0 Solving -251 + 5x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -62.75 + 1.25x + x2 = 0 Move the constant term to the right: Add '62.75' to each side of the equation. -62.75 + 1.25x + 62.75 + x2 = 0 + 62.75 Reorder the terms: -62.75 + 62.75 + 1.25x + x2 = 0 + 62.75 Combine like terms: -62.75 + 62.75 = 0.00 0.00 + 1.25x + x2 = 0 + 62.75 1.25x + x2 = 0 + 62.75 Combine like terms: 0 + 62.75 = 62.75 1.25x + x2 = 62.75 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 62.75 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 62.75 + 0.390625 Combine like terms: 62.75 + 0.390625 = 63.140625 0.390625 + 1.25x + x2 = 63.140625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 63.140625 Calculate the square root of the right side: 7.946107538 Break this problem into two subproblems by setting (x + 0.625) equal to 7.946107538 and -7.946107538.Subproblem 1
x + 0.625 = 7.946107538 Simplifying x + 0.625 = 7.946107538 Reorder the terms: 0.625 + x = 7.946107538 Solving 0.625 + x = 7.946107538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 7.946107538 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 7.946107538 + -0.625 x = 7.946107538 + -0.625 Combine like terms: 7.946107538 + -0.625 = 7.321107538 x = 7.321107538 Simplifying x = 7.321107538Subproblem 2
x + 0.625 = -7.946107538 Simplifying x + 0.625 = -7.946107538 Reorder the terms: 0.625 + x = -7.946107538 Solving 0.625 + x = -7.946107538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -7.946107538 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -7.946107538 + -0.625 x = -7.946107538 + -0.625 Combine like terms: -7.946107538 + -0.625 = -8.571107538 x = -8.571107538 Simplifying x = -8.571107538Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.321107538, -8.571107538}
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