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Simplifying 4x2 + -10x + -33 = 0 Reorder the terms: -33 + -10x + 4x2 = 0 Solving -33 + -10x + 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'. -8.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -2.5x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -2.5x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -2.5x + x2 = 0 + 8.25 -2.5x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -2.5x + x2 = 8.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 8.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8.25 + 1.5625 Combine like terms: 8.25 + 1.5625 = 9.8125 1.5625 + -2.5x + x2 = 9.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (x + -1.25) equal to 3.132491022 and -3.132491022.Subproblem 1
x + -1.25 = 3.132491022 Simplifying x + -1.25 = 3.132491022 Reorder the terms: -1.25 + x = 3.132491022 Solving -1.25 + x = 3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.132491022 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.132491022 + 1.25 x = 3.132491022 + 1.25 Combine like terms: 3.132491022 + 1.25 = 4.382491022 x = 4.382491022 Simplifying x = 4.382491022Subproblem 2
x + -1.25 = -3.132491022 Simplifying x + -1.25 = -3.132491022 Reorder the terms: -1.25 + x = -3.132491022 Solving -1.25 + x = -3.132491022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.132491022 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.132491022 + 1.25 x = -3.132491022 + 1.25 Combine like terms: -3.132491022 + 1.25 = -1.882491022 x = -1.882491022 Simplifying x = -1.882491022Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.382491022, -1.882491022}
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