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Simplifying 4x2 + -33x + 37 = -8 + 1 Reorder the terms: 37 + -33x + 4x2 = -8 + 1 Combine like terms: -8 + 1 = -7 37 + -33x + 4x2 = -7 Solving 37 + -33x + 4x2 = -7 Solving for variable 'x'. Reorder the terms: 37 + 7 + -33x + 4x2 = -7 + 7 Combine like terms: 37 + 7 = 44 44 + -33x + 4x2 = -7 + 7 Combine like terms: -7 + 7 = 0 44 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 11 + -8.25x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -8.25x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -8.25x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -8.25x + x2 = 0 + -11 -8.25x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -8.25x + x2 = -11 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 = -11 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -11 + 17.015625 Combine like terms: -11 + 17.015625 = 6.015625 17.015625 + -8.25x + x2 = 6.015625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -4.125) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -4.125 = 2.452677109 Simplifying x + -4.125 = 2.452677109 Reorder the terms: -4.125 + x = 2.452677109 Solving -4.125 + x = 2.452677109 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 = 2.452677109 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 2.452677109 + 4.125 x = 2.452677109 + 4.125 Combine like terms: 2.452677109 + 4.125 = 6.577677109 x = 6.577677109 Simplifying x = 6.577677109Subproblem 2
x + -4.125 = -2.452677109 Simplifying x + -4.125 = -2.452677109 Reorder the terms: -4.125 + x = -2.452677109 Solving -4.125 + x = -2.452677109 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 = -2.452677109 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -2.452677109 + 4.125 x = -2.452677109 + 4.125 Combine like terms: -2.452677109 + 4.125 = 1.672322891 x = 1.672322891 Simplifying x = 1.672322891Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.577677109, 1.672322891}
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