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Simplifying 2x2 + 40.32x + -75 = 0 Reorder the terms: -75 + 40.32x + 2x2 = 0 Solving -75 + 40.32x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -37.5 + 20.16x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 20.16x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 20.16x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 20.16x + x2 = 0 + 37.5 20.16x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 20.16x + x2 = 37.5 The x term is 20.16x. Take half its coefficient (10.08). Square it (101.6064) and add it to both sides. Add '101.6064' to each side of the equation. 20.16x + 101.6064 + x2 = 37.5 + 101.6064 Reorder the terms: 101.6064 + 20.16x + x2 = 37.5 + 101.6064 Combine like terms: 37.5 + 101.6064 = 139.1064 101.6064 + 20.16x + x2 = 139.1064 Factor a perfect square on the left side: (x + 10.08)(x + 10.08) = 139.1064 Calculate the square root of the right side: 11.794337624 Break this problem into two subproblems by setting (x + 10.08) equal to 11.794337624 and -11.794337624.Subproblem 1
x + 10.08 = 11.794337624 Simplifying x + 10.08 = 11.794337624 Reorder the terms: 10.08 + x = 11.794337624 Solving 10.08 + x = 11.794337624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.08' to each side of the equation. 10.08 + -10.08 + x = 11.794337624 + -10.08 Combine like terms: 10.08 + -10.08 = 0.00 0.00 + x = 11.794337624 + -10.08 x = 11.794337624 + -10.08 Combine like terms: 11.794337624 + -10.08 = 1.714337624 x = 1.714337624 Simplifying x = 1.714337624Subproblem 2
x + 10.08 = -11.794337624 Simplifying x + 10.08 = -11.794337624 Reorder the terms: 10.08 + x = -11.794337624 Solving 10.08 + x = -11.794337624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.08' to each side of the equation. 10.08 + -10.08 + x = -11.794337624 + -10.08 Combine like terms: 10.08 + -10.08 = 0.00 0.00 + x = -11.794337624 + -10.08 x = -11.794337624 + -10.08 Combine like terms: -11.794337624 + -10.08 = -21.874337624 x = -21.874337624 Simplifying x = -21.874337624Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.714337624, -21.874337624}
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