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Simplifying 2x2 = 25x + 33 Reorder the terms: 2x2 = 33 + 25x Solving 2x2 = 33 + 25x Solving for variable 'x'. Reorder the terms: -33 + -25x + 2x2 = 33 + 25x + -33 + -25x Reorder the terms: -33 + -25x + 2x2 = 33 + -33 + 25x + -25x Combine like terms: 33 + -33 = 0 -33 + -25x + 2x2 = 0 + 25x + -25x -33 + -25x + 2x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -33 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -12.5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -12.5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -12.5x + x2 = 0 + 16.5 -12.5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -12.5x + x2 = 16.5 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 16.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 16.5 + 39.0625 Combine like terms: 16.5 + 39.0625 = 55.5625 39.0625 + -12.5x + x2 = 55.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 55.5625 Calculate the square root of the right side: 7.454025758 Break this problem into two subproblems by setting (x + -6.25) equal to 7.454025758 and -7.454025758.Subproblem 1
x + -6.25 = 7.454025758 Simplifying x + -6.25 = 7.454025758 Reorder the terms: -6.25 + x = 7.454025758 Solving -6.25 + x = 7.454025758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 7.454025758 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.454025758 + 6.25 x = 7.454025758 + 6.25 Combine like terms: 7.454025758 + 6.25 = 13.704025758 x = 13.704025758 Simplifying x = 13.704025758Subproblem 2
x + -6.25 = -7.454025758 Simplifying x + -6.25 = -7.454025758 Reorder the terms: -6.25 + x = -7.454025758 Solving -6.25 + x = -7.454025758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -7.454025758 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.454025758 + 6.25 x = -7.454025758 + 6.25 Combine like terms: -7.454025758 + 6.25 = -1.204025758 x = -1.204025758 Simplifying x = -1.204025758Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.704025758, -1.204025758}
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