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Simplifying 71x2 + 18x + -9 = 0 Reorder the terms: -9 + 18x + 71x2 = 0 Solving -9 + 18x + 71x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 71 the coefficient of the squared term: Divide each side by '71'. -0.1267605634 + 0.2535211268x + x2 = 0 Move the constant term to the right: Add '0.1267605634' to each side of the equation. -0.1267605634 + 0.2535211268x + 0.1267605634 + x2 = 0 + 0.1267605634 Reorder the terms: -0.1267605634 + 0.1267605634 + 0.2535211268x + x2 = 0 + 0.1267605634 Combine like terms: -0.1267605634 + 0.1267605634 = 0.0000000000 0.0000000000 + 0.2535211268x + x2 = 0 + 0.1267605634 0.2535211268x + x2 = 0 + 0.1267605634 Combine like terms: 0 + 0.1267605634 = 0.1267605634 0.2535211268x + x2 = 0.1267605634 The x term is 0.2535211268x. Take half its coefficient (0.1267605634). Square it (0.01606824043) and add it to both sides. Add '0.01606824043' to each side of the equation. 0.2535211268x + 0.01606824043 + x2 = 0.1267605634 + 0.01606824043 Reorder the terms: 0.01606824043 + 0.2535211268x + x2 = 0.1267605634 + 0.01606824043 Combine like terms: 0.1267605634 + 0.01606824043 = 0.14282880383 0.01606824043 + 0.2535211268x + x2 = 0.14282880383 Factor a perfect square on the left side: (x + 0.1267605634)(x + 0.1267605634) = 0.14282880383 Calculate the square root of the right side: 0.377926982 Break this problem into two subproblems by setting (x + 0.1267605634) equal to 0.377926982 and -0.377926982.Subproblem 1
x + 0.1267605634 = 0.377926982 Simplifying x + 0.1267605634 = 0.377926982 Reorder the terms: 0.1267605634 + x = 0.377926982 Solving 0.1267605634 + x = 0.377926982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1267605634' to each side of the equation. 0.1267605634 + -0.1267605634 + x = 0.377926982 + -0.1267605634 Combine like terms: 0.1267605634 + -0.1267605634 = 0.0000000000 0.0000000000 + x = 0.377926982 + -0.1267605634 x = 0.377926982 + -0.1267605634 Combine like terms: 0.377926982 + -0.1267605634 = 0.2511664186 x = 0.2511664186 Simplifying x = 0.2511664186Subproblem 2
x + 0.1267605634 = -0.377926982 Simplifying x + 0.1267605634 = -0.377926982 Reorder the terms: 0.1267605634 + x = -0.377926982 Solving 0.1267605634 + x = -0.377926982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1267605634' to each side of the equation. 0.1267605634 + -0.1267605634 + x = -0.377926982 + -0.1267605634 Combine like terms: 0.1267605634 + -0.1267605634 = 0.0000000000 0.0000000000 + x = -0.377926982 + -0.1267605634 x = -0.377926982 + -0.1267605634 Combine like terms: -0.377926982 + -0.1267605634 = -0.5046875454 x = -0.5046875454 Simplifying x = -0.5046875454Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2511664186, -0.5046875454}
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