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Simplifying 20x2 + 39x + 15 = 0 Reorder the terms: 15 + 39x + 20x2 = 0 Solving 15 + 39x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.75 + 1.95x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.95x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.95x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.95x + x2 = 0 + -0.75 1.95x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.95x + x2 = -0.75 The x term is 1.95x. Take half its coefficient (0.975). Square it (0.950625) and add it to both sides. Add '0.950625' to each side of the equation. 1.95x + 0.950625 + x2 = -0.75 + 0.950625 Reorder the terms: 0.950625 + 1.95x + x2 = -0.75 + 0.950625 Combine like terms: -0.75 + 0.950625 = 0.200625 0.950625 + 1.95x + x2 = 0.200625 Factor a perfect square on the left side: (x + 0.975)(x + 0.975) = 0.200625 Calculate the square root of the right side: 0.447911822 Break this problem into two subproblems by setting (x + 0.975) equal to 0.447911822 and -0.447911822.Subproblem 1
x + 0.975 = 0.447911822 Simplifying x + 0.975 = 0.447911822 Reorder the terms: 0.975 + x = 0.447911822 Solving 0.975 + x = 0.447911822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.975' to each side of the equation. 0.975 + -0.975 + x = 0.447911822 + -0.975 Combine like terms: 0.975 + -0.975 = 0.000 0.000 + x = 0.447911822 + -0.975 x = 0.447911822 + -0.975 Combine like terms: 0.447911822 + -0.975 = -0.527088178 x = -0.527088178 Simplifying x = -0.527088178Subproblem 2
x + 0.975 = -0.447911822 Simplifying x + 0.975 = -0.447911822 Reorder the terms: 0.975 + x = -0.447911822 Solving 0.975 + x = -0.447911822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.975' to each side of the equation. 0.975 + -0.975 + x = -0.447911822 + -0.975 Combine like terms: 0.975 + -0.975 = 0.000 0.000 + x = -0.447911822 + -0.975 x = -0.447911822 + -0.975 Combine like terms: -0.447911822 + -0.975 = -1.422911822 x = -1.422911822 Simplifying x = -1.422911822Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.527088178, -1.422911822}
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