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Simplifying 0 = 2x2 + 33x + -65 Reorder the terms: 0 = -65 + 33x + 2x2 Solving 0 = -65 + 33x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 65 = 65 65 + -33x + -2x2 = -65 + 33x + 2x2 + 65 + -33x + -2x2 Reorder the terms: 65 + -33x + -2x2 = -65 + 65 + 33x + -33x + 2x2 + -2x2 Combine like terms: -65 + 65 = 0 65 + -33x + -2x2 = 0 + 33x + -33x + 2x2 + -2x2 65 + -33x + -2x2 = 33x + -33x + 2x2 + -2x2 Combine like terms: 33x + -33x = 0 65 + -33x + -2x2 = 0 + 2x2 + -2x2 65 + -33x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 65 + -33x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -32.5 + 16.5x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 16.5x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 16.5x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 16.5x + x2 = 0 + 32.5 16.5x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 16.5x + x2 = 32.5 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = 32.5 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 32.5 + 68.0625 Combine like terms: 32.5 + 68.0625 = 100.5625 68.0625 + 16.5x + x2 = 100.5625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 100.5625 Calculate the square root of the right side: 10.02808556 Break this problem into two subproblems by setting (x + 8.25) equal to 10.02808556 and -10.02808556.Subproblem 1
x + 8.25 = 10.02808556 Simplifying x + 8.25 = 10.02808556 Reorder the terms: 8.25 + x = 10.02808556 Solving 8.25 + x = 10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 10.02808556 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 10.02808556 + -8.25 x = 10.02808556 + -8.25 Combine like terms: 10.02808556 + -8.25 = 1.77808556 x = 1.77808556 Simplifying x = 1.77808556Subproblem 2
x + 8.25 = -10.02808556 Simplifying x + 8.25 = -10.02808556 Reorder the terms: 8.25 + x = -10.02808556 Solving 8.25 + x = -10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -10.02808556 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -10.02808556 + -8.25 x = -10.02808556 + -8.25 Combine like terms: -10.02808556 + -8.25 = -18.27808556 x = -18.27808556 Simplifying x = -18.27808556Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.77808556, -18.27808556}
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