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Simplifying 4x2 + 35x + 59 = 0 Reorder the terms: 59 + 35x + 4x2 = 0 Solving 59 + 35x + 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'. 14.75 + 8.75x + x2 = 0 Move the constant term to the right: Add '-14.75' to each side of the equation. 14.75 + 8.75x + -14.75 + x2 = 0 + -14.75 Reorder the terms: 14.75 + -14.75 + 8.75x + x2 = 0 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + 8.75x + x2 = 0 + -14.75 8.75x + x2 = 0 + -14.75 Combine like terms: 0 + -14.75 = -14.75 8.75x + x2 = -14.75 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = -14.75 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -14.75 + 19.140625 Combine like terms: -14.75 + 19.140625 = 4.390625 19.140625 + 8.75x + x2 = 4.390625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + 4.375) equal to 2.095381827 and -2.095381827.Subproblem 1
x + 4.375 = 2.095381827 Simplifying x + 4.375 = 2.095381827 Reorder the terms: 4.375 + x = 2.095381827 Solving 4.375 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 2.095381827 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 2.095381827 + -4.375 x = 2.095381827 + -4.375 Combine like terms: 2.095381827 + -4.375 = -2.279618173 x = -2.279618173 Simplifying x = -2.279618173Subproblem 2
x + 4.375 = -2.095381827 Simplifying x + 4.375 = -2.095381827 Reorder the terms: 4.375 + x = -2.095381827 Solving 4.375 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -2.095381827 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -2.095381827 + -4.375 x = -2.095381827 + -4.375 Combine like terms: -2.095381827 + -4.375 = -6.470381827 x = -6.470381827 Simplifying x = -6.470381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.279618173, -6.470381827}
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