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Simplifying 4x2 + 29x + -322 = 0 Reorder the terms: -322 + 29x + 4x2 = 0 Solving -322 + 29x + 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'. -80.5 + 7.25x + x2 = 0 Move the constant term to the right: Add '80.5' to each side of the equation. -80.5 + 7.25x + 80.5 + x2 = 0 + 80.5 Reorder the terms: -80.5 + 80.5 + 7.25x + x2 = 0 + 80.5 Combine like terms: -80.5 + 80.5 = 0.0 0.0 + 7.25x + x2 = 0 + 80.5 7.25x + x2 = 0 + 80.5 Combine like terms: 0 + 80.5 = 80.5 7.25x + x2 = 80.5 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 80.5 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 80.5 + 13.140625 Combine like terms: 80.5 + 13.140625 = 93.640625 13.140625 + 7.25x + x2 = 93.640625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 93.640625 Calculate the square root of the right side: 9.676808616 Break this problem into two subproblems by setting (x + 3.625) equal to 9.676808616 and -9.676808616.Subproblem 1
x + 3.625 = 9.676808616 Simplifying x + 3.625 = 9.676808616 Reorder the terms: 3.625 + x = 9.676808616 Solving 3.625 + x = 9.676808616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 9.676808616 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 9.676808616 + -3.625 x = 9.676808616 + -3.625 Combine like terms: 9.676808616 + -3.625 = 6.051808616 x = 6.051808616 Simplifying x = 6.051808616Subproblem 2
x + 3.625 = -9.676808616 Simplifying x + 3.625 = -9.676808616 Reorder the terms: 3.625 + x = -9.676808616 Solving 3.625 + x = -9.676808616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -9.676808616 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -9.676808616 + -3.625 x = -9.676808616 + -3.625 Combine like terms: -9.676808616 + -3.625 = -13.301808616 x = -13.301808616 Simplifying x = -13.301808616Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.051808616, -13.301808616}
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