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Simplifying 2x2 + 40x + 75 = 0 Reorder the terms: 75 + 40x + 2x2 = 0 Solving 75 + 40x + 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 + 20x + x2 = 0 Move the constant term to the right: Add '-37.5' to each side of the equation. 37.5 + 20x + -37.5 + x2 = 0 + -37.5 Reorder the terms: 37.5 + -37.5 + 20x + x2 = 0 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + 20x + x2 = 0 + -37.5 20x + x2 = 0 + -37.5 Combine like terms: 0 + -37.5 = -37.5 20x + x2 = -37.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -37.5 + 100 Reorder the terms: 100 + 20x + x2 = -37.5 + 100 Combine like terms: -37.5 + 100 = 62.5 100 + 20x + x2 = 62.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + 10) equal to 7.90569415 and -7.90569415.Subproblem 1
x + 10 = 7.90569415 Simplifying x + 10 = 7.90569415 Reorder the terms: 10 + x = 7.90569415 Solving 10 + x = 7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 7.90569415 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.90569415 + -10 x = 7.90569415 + -10 Combine like terms: 7.90569415 + -10 = -2.09430585 x = -2.09430585 Simplifying x = -2.09430585Subproblem 2
x + 10 = -7.90569415 Simplifying x + 10 = -7.90569415 Reorder the terms: 10 + x = -7.90569415 Solving 10 + x = -7.90569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -7.90569415 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.90569415 + -10 x = -7.90569415 + -10 Combine like terms: -7.90569415 + -10 = -17.90569415 x = -17.90569415 Simplifying x = -17.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.09430585, -17.90569415}
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