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Simplifying 4x2 + 5x + -145 = 0 Reorder the terms: -145 + 5x + 4x2 = 0 Solving -145 + 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'. -36.25 + 1.25x + x2 = 0 Move the constant term to the right: Add '36.25' to each side of the equation. -36.25 + 1.25x + 36.25 + x2 = 0 + 36.25 Reorder the terms: -36.25 + 36.25 + 1.25x + x2 = 0 + 36.25 Combine like terms: -36.25 + 36.25 = 0.00 0.00 + 1.25x + x2 = 0 + 36.25 1.25x + x2 = 0 + 36.25 Combine like terms: 0 + 36.25 = 36.25 1.25x + x2 = 36.25 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 = 36.25 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 36.25 + 0.390625 Combine like terms: 36.25 + 0.390625 = 36.640625 0.390625 + 1.25x + x2 = 36.640625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 36.640625 Calculate the square root of the right side: 6.053150006 Break this problem into two subproblems by setting (x + 0.625) equal to 6.053150006 and -6.053150006.Subproblem 1
x + 0.625 = 6.053150006 Simplifying x + 0.625 = 6.053150006 Reorder the terms: 0.625 + x = 6.053150006 Solving 0.625 + x = 6.053150006 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 = 6.053150006 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 6.053150006 + -0.625 x = 6.053150006 + -0.625 Combine like terms: 6.053150006 + -0.625 = 5.428150006 x = 5.428150006 Simplifying x = 5.428150006Subproblem 2
x + 0.625 = -6.053150006 Simplifying x + 0.625 = -6.053150006 Reorder the terms: 0.625 + x = -6.053150006 Solving 0.625 + x = -6.053150006 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 = -6.053150006 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -6.053150006 + -0.625 x = -6.053150006 + -0.625 Combine like terms: -6.053150006 + -0.625 = -6.678150006 x = -6.678150006 Simplifying x = -6.678150006Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.428150006, -6.678150006}
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