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Simplifying 2x2 + 40x + 15 = 0 Reorder the terms: 15 + 40x + 2x2 = 0 Solving 15 + 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'. 7.5 + 20x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 20x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 20x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 20x + x2 = 0 + -7.5 20x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 20x + x2 = -7.5 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 = -7.5 + 100 Reorder the terms: 100 + 20x + x2 = -7.5 + 100 Combine like terms: -7.5 + 100 = 92.5 100 + 20x + x2 = 92.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 92.5 Calculate the square root of the right side: 9.617692031 Break this problem into two subproblems by setting (x + 10) equal to 9.617692031 and -9.617692031.Subproblem 1
x + 10 = 9.617692031 Simplifying x + 10 = 9.617692031 Reorder the terms: 10 + x = 9.617692031 Solving 10 + x = 9.617692031 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 = 9.617692031 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.617692031 + -10 x = 9.617692031 + -10 Combine like terms: 9.617692031 + -10 = -0.382307969 x = -0.382307969 Simplifying x = -0.382307969Subproblem 2
x + 10 = -9.617692031 Simplifying x + 10 = -9.617692031 Reorder the terms: 10 + x = -9.617692031 Solving 10 + x = -9.617692031 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 = -9.617692031 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.617692031 + -10 x = -9.617692031 + -10 Combine like terms: -9.617692031 + -10 = -19.617692031 x = -19.617692031 Simplifying x = -19.617692031Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.382307969, -19.617692031}
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