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Simplifying 4x2 + -33x + 37 = 9x + 2 Reorder the terms: 37 + -33x + 4x2 = 9x + 2 Reorder the terms: 37 + -33x + 4x2 = 2 + 9x Solving 37 + -33x + 4x2 = 2 + 9x Solving for variable 'x'. Reorder the terms: 37 + -2 + -33x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: 37 + -2 = 35 35 + -33x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: -33x + -9x = -42x 35 + -42x + 4x2 = 2 + 9x + -2 + -9x Reorder the terms: 35 + -42x + 4x2 = 2 + -2 + 9x + -9x Combine like terms: 2 + -2 = 0 35 + -42x + 4x2 = 0 + 9x + -9x 35 + -42x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 35 + -42x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.75 + -10.5x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + -10.5x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + -10.5x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + -10.5x + x2 = 0 + -8.75 -10.5x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 -10.5x + x2 = -8.75 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -8.75 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -8.75 + 27.5625 Combine like terms: -8.75 + 27.5625 = 18.8125 27.5625 + -10.5x + x2 = 18.8125 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 18.8125 Calculate the square root of the right side: 4.337337893 Break this problem into two subproblems by setting (x + -5.25) equal to 4.337337893 and -4.337337893.Subproblem 1
x + -5.25 = 4.337337893 Simplifying x + -5.25 = 4.337337893 Reorder the terms: -5.25 + x = 4.337337893 Solving -5.25 + x = 4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.337337893 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.337337893 + 5.25 x = 4.337337893 + 5.25 Combine like terms: 4.337337893 + 5.25 = 9.587337893 x = 9.587337893 Simplifying x = 9.587337893Subproblem 2
x + -5.25 = -4.337337893 Simplifying x + -5.25 = -4.337337893 Reorder the terms: -5.25 + x = -4.337337893 Solving -5.25 + x = -4.337337893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.337337893 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.337337893 + 5.25 x = -4.337337893 + 5.25 Combine like terms: -4.337337893 + 5.25 = 0.912662107 x = 0.912662107 Simplifying x = 0.912662107Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.587337893, 0.912662107}
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