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Simplifying 19.63x2 + -127.4x + 25.98 = 0 Reorder the terms: 25.98 + -127.4x + 19.63x2 = 0 Solving 25.98 + -127.4x + 19.63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19.63 the coefficient of the squared term: Divide each side by '19.63'. 1.323484463 + -6.490066225x + x2 = 0 Move the constant term to the right: Add '-1.323484463' to each side of the equation. 1.323484463 + -6.490066225x + -1.323484463 + x2 = 0 + -1.323484463 Reorder the terms: 1.323484463 + -1.323484463 + -6.490066225x + x2 = 0 + -1.323484463 Combine like terms: 1.323484463 + -1.323484463 = 0.000000000 0.000000000 + -6.490066225x + x2 = 0 + -1.323484463 -6.490066225x + x2 = 0 + -1.323484463 Combine like terms: 0 + -1.323484463 = -1.323484463 -6.490066225x + x2 = -1.323484463 The x term is -6.490066225x. Take half its coefficient (-3.245033113). Square it (10.53023990) and add it to both sides. Add '10.53023990' to each side of the equation. -6.490066225x + 10.53023990 + x2 = -1.323484463 + 10.53023990 Reorder the terms: 10.53023990 + -6.490066225x + x2 = -1.323484463 + 10.53023990 Combine like terms: -1.323484463 + 10.53023990 = 9.206755437 10.53023990 + -6.490066225x + x2 = 9.206755437 Factor a perfect square on the left side: (x + -3.245033113)(x + -3.245033113) = 9.206755437 Calculate the square root of the right side: 3.034263574 Break this problem into two subproblems by setting (x + -3.245033113) equal to 3.034263574 and -3.034263574.Subproblem 1
x + -3.245033113 = 3.034263574 Simplifying x + -3.245033113 = 3.034263574 Reorder the terms: -3.245033113 + x = 3.034263574 Solving -3.245033113 + x = 3.034263574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.245033113' to each side of the equation. -3.245033113 + 3.245033113 + x = 3.034263574 + 3.245033113 Combine like terms: -3.245033113 + 3.245033113 = 0.000000000 0.000000000 + x = 3.034263574 + 3.245033113 x = 3.034263574 + 3.245033113 Combine like terms: 3.034263574 + 3.245033113 = 6.279296687 x = 6.279296687 Simplifying x = 6.279296687Subproblem 2
x + -3.245033113 = -3.034263574 Simplifying x + -3.245033113 = -3.034263574 Reorder the terms: -3.245033113 + x = -3.034263574 Solving -3.245033113 + x = -3.034263574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.245033113' to each side of the equation. -3.245033113 + 3.245033113 + x = -3.034263574 + 3.245033113 Combine like terms: -3.245033113 + 3.245033113 = 0.000000000 0.000000000 + x = -3.034263574 + 3.245033113 x = -3.034263574 + 3.245033113 Combine like terms: -3.034263574 + 3.245033113 = 0.210769539 x = 0.210769539 Simplifying x = 0.210769539Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.279296687, 0.210769539}
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