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Simplifying 4x2 + -33x + 52 = 0 Reorder the terms: 52 + -33x + 4x2 = 0 Solving 52 + -33x + 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 + -8.25x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8.25x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8.25x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8.25x + x2 = 0 + -13 -8.25x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8.25x + x2 = -13 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -13 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -13 + 17.015625 Combine like terms: -13 + 17.015625 = 4.015625 17.015625 + -8.25x + x2 = 4.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + -4.125) equal to 2.003902443 and -2.003902443.Subproblem 1
x + -4.125 = 2.003902443 Simplifying x + -4.125 = 2.003902443 Reorder the terms: -4.125 + x = 2.003902443 Solving -4.125 + x = 2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 2.003902443 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 2.003902443 + 4.125 x = 2.003902443 + 4.125 Combine like terms: 2.003902443 + 4.125 = 6.128902443 x = 6.128902443 Simplifying x = 6.128902443Subproblem 2
x + -4.125 = -2.003902443 Simplifying x + -4.125 = -2.003902443 Reorder the terms: -4.125 + x = -2.003902443 Solving -4.125 + x = -2.003902443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -2.003902443 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -2.003902443 + 4.125 x = -2.003902443 + 4.125 Combine like terms: -2.003902443 + 4.125 = 2.121097557 x = 2.121097557 Simplifying x = 2.121097557Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.128902443, 2.121097557}
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