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Simplifying 4x2 + 5x + -52 = 0 Reorder the terms: -52 + 5x + 4x2 = 0 Solving -52 + 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'. -13 + 1.25x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 1.25x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 1.25x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 1.25x + x2 = 0 + 13 1.25x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 1.25x + x2 = 13 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 = 13 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 13 + 0.390625 Combine like terms: 13 + 0.390625 = 13.390625 0.390625 + 1.25x + x2 = 13.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 13.390625 Calculate the square root of the right side: 3.659320292 Break this problem into two subproblems by setting (x + 0.625) equal to 3.659320292 and -3.659320292.Subproblem 1
x + 0.625 = 3.659320292 Simplifying x + 0.625 = 3.659320292 Reorder the terms: 0.625 + x = 3.659320292 Solving 0.625 + x = 3.659320292 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 = 3.659320292 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.659320292 + -0.625 x = 3.659320292 + -0.625 Combine like terms: 3.659320292 + -0.625 = 3.034320292 x = 3.034320292 Simplifying x = 3.034320292Subproblem 2
x + 0.625 = -3.659320292 Simplifying x + 0.625 = -3.659320292 Reorder the terms: 0.625 + x = -3.659320292 Solving 0.625 + x = -3.659320292 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 = -3.659320292 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.659320292 + -0.625 x = -3.659320292 + -0.625 Combine like terms: -3.659320292 + -0.625 = -4.284320292 x = -4.284320292 Simplifying x = -4.284320292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.034320292, -4.284320292}
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