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Simplifying 2x2 + 20x + -337.5 = 0 Reorder the terms: -337.5 + 20x + 2x2 = 0 Solving -337.5 + 20x + 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'. -168.75 + 10x + x2 = 0 Move the constant term to the right: Add '168.75' to each side of the equation. -168.75 + 10x + 168.75 + x2 = 0 + 168.75 Reorder the terms: -168.75 + 168.75 + 10x + x2 = 0 + 168.75 Combine like terms: -168.75 + 168.75 = 0.00 0.00 + 10x + x2 = 0 + 168.75 10x + x2 = 0 + 168.75 Combine like terms: 0 + 168.75 = 168.75 10x + x2 = 168.75 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 168.75 + 25 Reorder the terms: 25 + 10x + x2 = 168.75 + 25 Combine like terms: 168.75 + 25 = 193.75 25 + 10x + x2 = 193.75 Factor a perfect square on the left side: (x + 5)(x + 5) = 193.75 Calculate the square root of the right side: 13.919410907 Break this problem into two subproblems by setting (x + 5) equal to 13.919410907 and -13.919410907.Subproblem 1
x + 5 = 13.919410907 Simplifying x + 5 = 13.919410907 Reorder the terms: 5 + x = 13.919410907 Solving 5 + x = 13.919410907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 13.919410907 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.919410907 + -5 x = 13.919410907 + -5 Combine like terms: 13.919410907 + -5 = 8.919410907 x = 8.919410907 Simplifying x = 8.919410907Subproblem 2
x + 5 = -13.919410907 Simplifying x + 5 = -13.919410907 Reorder the terms: 5 + x = -13.919410907 Solving 5 + x = -13.919410907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -13.919410907 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.919410907 + -5 x = -13.919410907 + -5 Combine like terms: -13.919410907 + -5 = -18.919410907 x = -18.919410907 Simplifying x = -18.919410907Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.919410907, -18.919410907}
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