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Simplifying 5x2 + -33x = -25 Reorder the terms: -33x + 5x2 = -25 Solving -33x + 5x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + -33x + 5x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -33x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5 + -6.6x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6.6x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -6.6x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6.6x + x2 = 0 + -5 -6.6x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6.6x + x2 = -5 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -5 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -5 + 10.89 Combine like terms: -5 + 10.89 = 5.89 10.89 + -6.6x + x2 = 5.89 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 5.89 Calculate the square root of the right side: 2.42693222 Break this problem into two subproblems by setting (x + -3.3) equal to 2.42693222 and -2.42693222.Subproblem 1
x + -3.3 = 2.42693222 Simplifying x + -3.3 = 2.42693222 Reorder the terms: -3.3 + x = 2.42693222 Solving -3.3 + x = 2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 2.42693222 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 2.42693222 + 3.3 x = 2.42693222 + 3.3 Combine like terms: 2.42693222 + 3.3 = 5.72693222 x = 5.72693222 Simplifying x = 5.72693222Subproblem 2
x + -3.3 = -2.42693222 Simplifying x + -3.3 = -2.42693222 Reorder the terms: -3.3 + x = -2.42693222 Solving -3.3 + x = -2.42693222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -2.42693222 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -2.42693222 + 3.3 x = -2.42693222 + 3.3 Combine like terms: -2.42693222 + 3.3 = 0.87306778 x = 0.87306778 Simplifying x = 0.87306778Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.72693222, 0.87306778}
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