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Simplifying 8x2 + -9x + -140 = 3 Reorder the terms: -140 + -9x + 8x2 = 3 Solving -140 + -9x + 8x2 = 3 Solving for variable 'x'. Reorder the terms: -140 + -3 + -9x + 8x2 = 3 + -3 Combine like terms: -140 + -3 = -143 -143 + -9x + 8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -143 + -9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -17.875 + -1.125x + x2 = 0 Move the constant term to the right: Add '17.875' to each side of the equation. -17.875 + -1.125x + 17.875 + x2 = 0 + 17.875 Reorder the terms: -17.875 + 17.875 + -1.125x + x2 = 0 + 17.875 Combine like terms: -17.875 + 17.875 = 0.000 0.000 + -1.125x + x2 = 0 + 17.875 -1.125x + x2 = 0 + 17.875 Combine like terms: 0 + 17.875 = 17.875 -1.125x + x2 = 17.875 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 = 17.875 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 17.875 + 0.31640625 Combine like terms: 17.875 + 0.31640625 = 18.19140625 0.31640625 + -1.125x + x2 = 18.19140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 18.19140625 Calculate the square root of the right side: 4.26513848 Break this problem into two subproblems by setting (x + -0.5625) equal to 4.26513848 and -4.26513848.Subproblem 1
x + -0.5625 = 4.26513848 Simplifying x + -0.5625 = 4.26513848 Reorder the terms: -0.5625 + x = 4.26513848 Solving -0.5625 + x = 4.26513848 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 = 4.26513848 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 4.26513848 + 0.5625 x = 4.26513848 + 0.5625 Combine like terms: 4.26513848 + 0.5625 = 4.82763848 x = 4.82763848 Simplifying x = 4.82763848Subproblem 2
x + -0.5625 = -4.26513848 Simplifying x + -0.5625 = -4.26513848 Reorder the terms: -0.5625 + x = -4.26513848 Solving -0.5625 + x = -4.26513848 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 = -4.26513848 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -4.26513848 + 0.5625 x = -4.26513848 + 0.5625 Combine like terms: -4.26513848 + 0.5625 = -3.70263848 x = -3.70263848 Simplifying x = -3.70263848Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.82763848, -3.70263848}
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