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Simplifying 4x2 + -33x + -9 = 0 Reorder the terms: -9 + -33x + 4x2 = 0 Solving -9 + -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'. -2.25 + -8.25x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -8.25x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -8.25x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -8.25x + x2 = 0 + 2.25 -8.25x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -8.25x + x2 = 2.25 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 = 2.25 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = 2.25 + 17.015625 Combine like terms: 2.25 + 17.015625 = 19.265625 17.015625 + -8.25x + x2 = 19.265625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 19.265625 Calculate the square root of the right side: 4.389262467 Break this problem into two subproblems by setting (x + -4.125) equal to 4.389262467 and -4.389262467.Subproblem 1
x + -4.125 = 4.389262467 Simplifying x + -4.125 = 4.389262467 Reorder the terms: -4.125 + x = 4.389262467 Solving -4.125 + x = 4.389262467 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 = 4.389262467 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 4.389262467 + 4.125 x = 4.389262467 + 4.125 Combine like terms: 4.389262467 + 4.125 = 8.514262467 x = 8.514262467 Simplifying x = 8.514262467Subproblem 2
x + -4.125 = -4.389262467 Simplifying x + -4.125 = -4.389262467 Reorder the terms: -4.125 + x = -4.389262467 Solving -4.125 + x = -4.389262467 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 = -4.389262467 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -4.389262467 + 4.125 x = -4.389262467 + 4.125 Combine like terms: -4.389262467 + 4.125 = -0.264262467 x = -0.264262467 Simplifying x = -0.264262467Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.514262467, -0.264262467}
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