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Simplifying -40x2 + -47x + 12 = 0 Reorder the terms: 12 + -47x + -40x2 = 0 Solving 12 + -47x + -40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.3 + 1.175x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 1.175x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 1.175x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 1.175x + x2 = 0 + 0.3 1.175x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 1.175x + x2 = 0.3 The x term is 1.175x. Take half its coefficient (0.5875). Square it (0.34515625) and add it to both sides. Add '0.34515625' to each side of the equation. 1.175x + 0.34515625 + x2 = 0.3 + 0.34515625 Reorder the terms: 0.34515625 + 1.175x + x2 = 0.3 + 0.34515625 Combine like terms: 0.3 + 0.34515625 = 0.64515625 0.34515625 + 1.175x + x2 = 0.64515625 Factor a perfect square on the left side: (x + 0.5875)(x + 0.5875) = 0.64515625 Calculate the square root of the right side: 0.803216191 Break this problem into two subproblems by setting (x + 0.5875) equal to 0.803216191 and -0.803216191.Subproblem 1
x + 0.5875 = 0.803216191 Simplifying x + 0.5875 = 0.803216191 Reorder the terms: 0.5875 + x = 0.803216191 Solving 0.5875 + x = 0.803216191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5875' to each side of the equation. 0.5875 + -0.5875 + x = 0.803216191 + -0.5875 Combine like terms: 0.5875 + -0.5875 = 0.0000 0.0000 + x = 0.803216191 + -0.5875 x = 0.803216191 + -0.5875 Combine like terms: 0.803216191 + -0.5875 = 0.215716191 x = 0.215716191 Simplifying x = 0.215716191Subproblem 2
x + 0.5875 = -0.803216191 Simplifying x + 0.5875 = -0.803216191 Reorder the terms: 0.5875 + x = -0.803216191 Solving 0.5875 + x = -0.803216191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5875' to each side of the equation. 0.5875 + -0.5875 + x = -0.803216191 + -0.5875 Combine like terms: 0.5875 + -0.5875 = 0.0000 0.0000 + x = -0.803216191 + -0.5875 x = -0.803216191 + -0.5875 Combine like terms: -0.803216191 + -0.5875 = -1.390716191 x = -1.390716191 Simplifying x = -1.390716191Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.215716191, -1.390716191}
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