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Simplifying 5x(33 + -5x) = 33 (33 * 5x + -5x * 5x) = 33 (165x + -25x2) = 33 Solving 165x + -25x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + 165x + -25x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 165x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. 1.32 + -6.6x + x2 = 0 Move the constant term to the right: Add '-1.32' to each side of the equation. 1.32 + -6.6x + -1.32 + x2 = 0 + -1.32 Reorder the terms: 1.32 + -1.32 + -6.6x + x2 = 0 + -1.32 Combine like terms: 1.32 + -1.32 = 0.00 0.00 + -6.6x + x2 = 0 + -1.32 -6.6x + x2 = 0 + -1.32 Combine like terms: 0 + -1.32 = -1.32 -6.6x + x2 = -1.32 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 = -1.32 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -1.32 + 10.89 Combine like terms: -1.32 + 10.89 = 9.57 10.89 + -6.6x + x2 = 9.57 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 9.57 Calculate the square root of the right side: 3.09354166 Break this problem into two subproblems by setting (x + -3.3) equal to 3.09354166 and -3.09354166.Subproblem 1
x + -3.3 = 3.09354166 Simplifying x + -3.3 = 3.09354166 Reorder the terms: -3.3 + x = 3.09354166 Solving -3.3 + x = 3.09354166 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 = 3.09354166 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 3.09354166 + 3.3 x = 3.09354166 + 3.3 Combine like terms: 3.09354166 + 3.3 = 6.39354166 x = 6.39354166 Simplifying x = 6.39354166Subproblem 2
x + -3.3 = -3.09354166 Simplifying x + -3.3 = -3.09354166 Reorder the terms: -3.3 + x = -3.09354166 Solving -3.3 + x = -3.09354166 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 = -3.09354166 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -3.09354166 + 3.3 x = -3.09354166 + 3.3 Combine like terms: -3.09354166 + 3.3 = 0.20645834 x = 0.20645834 Simplifying x = 0.20645834Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.39354166, 0.20645834}
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