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Simplifying 2x2 + 45x + 200 = 0 Reorder the terms: 200 + 45x + 2x2 = 0 Solving 200 + 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'. 100 + 22.5x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + 22.5x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 22.5x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 22.5x + x2 = 0 + -100 22.5x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 22.5x + x2 = -100 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 = -100 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = -100 + 126.5625 Combine like terms: -100 + 126.5625 = 26.5625 126.5625 + 22.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + 11.25) equal to 5.153882032 and -5.153882032.Subproblem 1
x + 11.25 = 5.153882032 Simplifying x + 11.25 = 5.153882032 Reorder the terms: 11.25 + x = 5.153882032 Solving 11.25 + x = 5.153882032 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 = 5.153882032 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 5.153882032 + -11.25 x = 5.153882032 + -11.25 Combine like terms: 5.153882032 + -11.25 = -6.096117968 x = -6.096117968 Simplifying x = -6.096117968Subproblem 2
x + 11.25 = -5.153882032 Simplifying x + 11.25 = -5.153882032 Reorder the terms: 11.25 + x = -5.153882032 Solving 11.25 + x = -5.153882032 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 = -5.153882032 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -5.153882032 + -11.25 x = -5.153882032 + -11.25 Combine like terms: -5.153882032 + -11.25 = -16.403882032 x = -16.403882032 Simplifying x = -16.403882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.096117968, -16.403882032}
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