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Simplifying 25x2 + 12x + -15 = 0 Reorder the terms: -15 + 12x + 25x2 = 0 Solving -15 + 12x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.6 + 0.48x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.48x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.48x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.48x + x2 = 0 + 0.6 0.48x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.48x + x2 = 0.6 The x term is 0.48x. Take half its coefficient (0.24). Square it (0.0576) and add it to both sides. Add '0.0576' to each side of the equation. 0.48x + 0.0576 + x2 = 0.6 + 0.0576 Reorder the terms: 0.0576 + 0.48x + x2 = 0.6 + 0.0576 Combine like terms: 0.6 + 0.0576 = 0.6576 0.0576 + 0.48x + x2 = 0.6576 Factor a perfect square on the left side: (x + 0.24)(x + 0.24) = 0.6576 Calculate the square root of the right side: 0.810925397 Break this problem into two subproblems by setting (x + 0.24) equal to 0.810925397 and -0.810925397.Subproblem 1
x + 0.24 = 0.810925397 Simplifying x + 0.24 = 0.810925397 Reorder the terms: 0.24 + x = 0.810925397 Solving 0.24 + x = 0.810925397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.24' to each side of the equation. 0.24 + -0.24 + x = 0.810925397 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + x = 0.810925397 + -0.24 x = 0.810925397 + -0.24 Combine like terms: 0.810925397 + -0.24 = 0.570925397 x = 0.570925397 Simplifying x = 0.570925397Subproblem 2
x + 0.24 = -0.810925397 Simplifying x + 0.24 = -0.810925397 Reorder the terms: 0.24 + x = -0.810925397 Solving 0.24 + x = -0.810925397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.24' to each side of the equation. 0.24 + -0.24 + x = -0.810925397 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + x = -0.810925397 + -0.24 x = -0.810925397 + -0.24 Combine like terms: -0.810925397 + -0.24 = -1.050925397 x = -1.050925397 Simplifying x = -1.050925397Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.570925397, -1.050925397}
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