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Simplifying 8x2 + -9x + -120 = 0 Reorder the terms: -120 + -9x + 8x2 = 0 Solving -120 + -9x + 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 + -1.125x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -1.125x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -1.125x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1.125x + x2 = 0 + 15 -1.125x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1.125x + x2 = 15 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 15 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 15 + 0.31640625 Combine like terms: 15 + 0.31640625 = 15.31640625 0.31640625 + -1.125x + x2 = 15.31640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 15.31640625 Calculate the square root of the right side: 3.913618051 Break this problem into two subproblems by setting (x + -0.5625) equal to 3.913618051 and -3.913618051.Subproblem 1
x + -0.5625 = 3.913618051 Simplifying x + -0.5625 = 3.913618051 Reorder the terms: -0.5625 + x = 3.913618051 Solving -0.5625 + x = 3.913618051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 3.913618051 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 3.913618051 + 0.5625 x = 3.913618051 + 0.5625 Combine like terms: 3.913618051 + 0.5625 = 4.476118051 x = 4.476118051 Simplifying x = 4.476118051Subproblem 2
x + -0.5625 = -3.913618051 Simplifying x + -0.5625 = -3.913618051 Reorder the terms: -0.5625 + x = -3.913618051 Solving -0.5625 + x = -3.913618051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -3.913618051 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -3.913618051 + 0.5625 x = -3.913618051 + 0.5625 Combine like terms: -3.913618051 + 0.5625 = -3.351118051 x = -3.351118051 Simplifying x = -3.351118051Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.476118051, -3.351118051}
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