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Simplifying (8x2 + 9x + -87) = 0 Reorder the terms: (-87 + 9x + 8x2) = 0 Remove parenthesis around (-87 + 9x + 8x2) -87 + 9x + 8x2 = 0 Solving -87 + 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'. -10.875 + 1.125x + x2 = 0 Move the constant term to the right: Add '10.875' to each side of the equation. -10.875 + 1.125x + 10.875 + x2 = 0 + 10.875 Reorder the terms: -10.875 + 10.875 + 1.125x + x2 = 0 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + 1.125x + x2 = 0 + 10.875 1.125x + x2 = 0 + 10.875 Combine like terms: 0 + 10.875 = 10.875 1.125x + x2 = 10.875 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 = 10.875 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 10.875 + 0.31640625 Combine like terms: 10.875 + 0.31640625 = 11.19140625 0.31640625 + 1.125x + x2 = 11.19140625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 11.19140625 Calculate the square root of the right side: 3.345355923 Break this problem into two subproblems by setting (x + 0.5625) equal to 3.345355923 and -3.345355923.Subproblem 1
x + 0.5625 = 3.345355923 Simplifying x + 0.5625 = 3.345355923 Reorder the terms: 0.5625 + x = 3.345355923 Solving 0.5625 + x = 3.345355923 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 = 3.345355923 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 3.345355923 + -0.5625 x = 3.345355923 + -0.5625 Combine like terms: 3.345355923 + -0.5625 = 2.782855923 x = 2.782855923 Simplifying x = 2.782855923Subproblem 2
x + 0.5625 = -3.345355923 Simplifying x + 0.5625 = -3.345355923 Reorder the terms: 0.5625 + x = -3.345355923 Solving 0.5625 + x = -3.345355923 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 = -3.345355923 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -3.345355923 + -0.5625 x = -3.345355923 + -0.5625 Combine like terms: -3.345355923 + -0.5625 = -3.907855923 x = -3.907855923 Simplifying x = -3.907855923Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.782855923, -3.907855923}
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