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Simplifying 42x2 + -238x + -2465 = 0 Reorder the terms: -2465 + -238x + 42x2 = 0 Solving -2465 + -238x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -58.69047619 + -5.666666667x + x2 = 0 Move the constant term to the right: Add '58.69047619' to each side of the equation. -58.69047619 + -5.666666667x + 58.69047619 + x2 = 0 + 58.69047619 Reorder the terms: -58.69047619 + 58.69047619 + -5.666666667x + x2 = 0 + 58.69047619 Combine like terms: -58.69047619 + 58.69047619 = 0.00000000 0.00000000 + -5.666666667x + x2 = 0 + 58.69047619 -5.666666667x + x2 = 0 + 58.69047619 Combine like terms: 0 + 58.69047619 = 58.69047619 -5.666666667x + x2 = 58.69047619 The x term is -5.666666667x. Take half its coefficient (-2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. -5.666666667x + 8.027777782 + x2 = 58.69047619 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x + x2 = 58.69047619 + 8.027777782 Combine like terms: 58.69047619 + 8.027777782 = 66.718253972 8.027777782 + -5.666666667x + x2 = 66.718253972 Factor a perfect square on the left side: (x + -2.833333334)(x + -2.833333334) = 66.718253972 Calculate the square root of the right side: 8.168124263 Break this problem into two subproblems by setting (x + -2.833333334) equal to 8.168124263 and -8.168124263.Subproblem 1
x + -2.833333334 = 8.168124263 Simplifying x + -2.833333334 = 8.168124263 Reorder the terms: -2.833333334 + x = 8.168124263 Solving -2.833333334 + x = 8.168124263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 8.168124263 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 8.168124263 + 2.833333334 x = 8.168124263 + 2.833333334 Combine like terms: 8.168124263 + 2.833333334 = 11.001457597 x = 11.001457597 Simplifying x = 11.001457597Subproblem 2
x + -2.833333334 = -8.168124263 Simplifying x + -2.833333334 = -8.168124263 Reorder the terms: -2.833333334 + x = -8.168124263 Solving -2.833333334 + x = -8.168124263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -8.168124263 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -8.168124263 + 2.833333334 x = -8.168124263 + 2.833333334 Combine like terms: -8.168124263 + 2.833333334 = -5.334790929 x = -5.334790929 Simplifying x = -5.334790929Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.001457597, -5.334790929}
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