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Simplifying 2x2 + 45x + -500 = 0 Reorder the terms: -500 + 45x + 2x2 = 0 Solving -500 + 45x + 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'. -250 + 22.5x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + 22.5x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 22.5x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 22.5x + x2 = 0 + 250 22.5x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 22.5x + x2 = 250 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 250 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 250 + 126.5625 Combine like terms: 250 + 126.5625 = 376.5625 126.5625 + 22.5x + x2 = 376.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 376.5625 Calculate the square root of the right side: 19.40521837 Break this problem into two subproblems by setting (x + 11.25) equal to 19.40521837 and -19.40521837.Subproblem 1
x + 11.25 = 19.40521837 Simplifying x + 11.25 = 19.40521837 Reorder the terms: 11.25 + x = 19.40521837 Solving 11.25 + x = 19.40521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 19.40521837 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 19.40521837 + -11.25 x = 19.40521837 + -11.25 Combine like terms: 19.40521837 + -11.25 = 8.15521837 x = 8.15521837 Simplifying x = 8.15521837Subproblem 2
x + 11.25 = -19.40521837 Simplifying x + 11.25 = -19.40521837 Reorder the terms: 11.25 + x = -19.40521837 Solving 11.25 + x = -19.40521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -19.40521837 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -19.40521837 + -11.25 x = -19.40521837 + -11.25 Combine like terms: -19.40521837 + -11.25 = -30.65521837 x = -30.65521837 Simplifying x = -30.65521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.15521837, -30.65521837}
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