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Simplifying 3x2 + 215x + 308 = 0 Reorder the terms: 308 + 215x + 3x2 = 0 Solving 308 + 215x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 102.6666667 + 71.66666667x + x2 = 0 Move the constant term to the right: Add '-102.6666667' to each side of the equation. 102.6666667 + 71.66666667x + -102.6666667 + x2 = 0 + -102.6666667 Reorder the terms: 102.6666667 + -102.6666667 + 71.66666667x + x2 = 0 + -102.6666667 Combine like terms: 102.6666667 + -102.6666667 = 0.0000000 0.0000000 + 71.66666667x + x2 = 0 + -102.6666667 71.66666667x + x2 = 0 + -102.6666667 Combine like terms: 0 + -102.6666667 = -102.6666667 71.66666667x + x2 = -102.6666667 The x term is 71.66666667x. Take half its coefficient (35.83333334). Square it (1284.027778) and add it to both sides. Add '1284.027778' to each side of the equation. 71.66666667x + 1284.027778 + x2 = -102.6666667 + 1284.027778 Reorder the terms: 1284.027778 + 71.66666667x + x2 = -102.6666667 + 1284.027778 Combine like terms: -102.6666667 + 1284.027778 = 1181.3611113 1284.027778 + 71.66666667x + x2 = 1181.3611113 Factor a perfect square on the left side: (x + 35.83333334)(x + 35.83333334) = 1181.3611113 Calculate the square root of the right side: 34.370934106 Break this problem into two subproblems by setting (x + 35.83333334) equal to 34.370934106 and -34.370934106.Subproblem 1
x + 35.83333334 = 34.370934106 Simplifying x + 35.83333334 = 34.370934106 Reorder the terms: 35.83333334 + x = 34.370934106 Solving 35.83333334 + x = 34.370934106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.83333334' to each side of the equation. 35.83333334 + -35.83333334 + x = 34.370934106 + -35.83333334 Combine like terms: 35.83333334 + -35.83333334 = 0.00000000 0.00000000 + x = 34.370934106 + -35.83333334 x = 34.370934106 + -35.83333334 Combine like terms: 34.370934106 + -35.83333334 = -1.462399234 x = -1.462399234 Simplifying x = -1.462399234Subproblem 2
x + 35.83333334 = -34.370934106 Simplifying x + 35.83333334 = -34.370934106 Reorder the terms: 35.83333334 + x = -34.370934106 Solving 35.83333334 + x = -34.370934106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.83333334' to each side of the equation. 35.83333334 + -35.83333334 + x = -34.370934106 + -35.83333334 Combine like terms: 35.83333334 + -35.83333334 = 0.00000000 0.00000000 + x = -34.370934106 + -35.83333334 x = -34.370934106 + -35.83333334 Combine like terms: -34.370934106 + -35.83333334 = -70.204267446 x = -70.204267446 Simplifying x = -70.204267446Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.462399234, -70.204267446}
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