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Simplifying 8x2 + -19x + -120 = 0 Reorder the terms: -120 + -19x + 8x2 = 0 Solving -120 + -19x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15 + -2.375x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -2.375x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -2.375x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2.375x + x2 = 0 + 15 -2.375x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -2.375x + x2 = 15 The x term is -2.375x. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375x + 1.41015625 + x2 = 15 + 1.41015625 Reorder the terms: 1.41015625 + -2.375x + x2 = 15 + 1.41015625 Combine like terms: 15 + 1.41015625 = 16.41015625 1.41015625 + -2.375x + x2 = 16.41015625 Factor a perfect square on the left side: (x + -1.1875)(x + -1.1875) = 16.41015625 Calculate the square root of the right side: 4.050945106 Break this problem into two subproblems by setting (x + -1.1875) equal to 4.050945106 and -4.050945106.Subproblem 1
x + -1.1875 = 4.050945106 Simplifying x + -1.1875 = 4.050945106 Reorder the terms: -1.1875 + x = 4.050945106 Solving -1.1875 + x = 4.050945106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = 4.050945106 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 4.050945106 + 1.1875 x = 4.050945106 + 1.1875 Combine like terms: 4.050945106 + 1.1875 = 5.238445106 x = 5.238445106 Simplifying x = 5.238445106Subproblem 2
x + -1.1875 = -4.050945106 Simplifying x + -1.1875 = -4.050945106 Reorder the terms: -1.1875 + x = -4.050945106 Solving -1.1875 + x = -4.050945106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = -4.050945106 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -4.050945106 + 1.1875 x = -4.050945106 + 1.1875 Combine like terms: -4.050945106 + 1.1875 = -2.863445106 x = -2.863445106 Simplifying x = -2.863445106Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.238445106, -2.863445106}
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