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Simplifying 8x2 + -9x + -32 = 0 Reorder the terms: -32 + -9x + 8x2 = 0 Solving -32 + -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'. -4 + -1.125x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.125x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.125x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.125x + x2 = 0 + 4 -1.125x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.125x + x2 = 4 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 = 4 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 4 + 0.31640625 Combine like terms: 4 + 0.31640625 = 4.31640625 0.31640625 + -1.125x + x2 = 4.31640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 4.31640625 Calculate the square root of the right side: 2.077596267 Break this problem into two subproblems by setting (x + -0.5625) equal to 2.077596267 and -2.077596267.Subproblem 1
x + -0.5625 = 2.077596267 Simplifying x + -0.5625 = 2.077596267 Reorder the terms: -0.5625 + x = 2.077596267 Solving -0.5625 + x = 2.077596267 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 = 2.077596267 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 2.077596267 + 0.5625 x = 2.077596267 + 0.5625 Combine like terms: 2.077596267 + 0.5625 = 2.640096267 x = 2.640096267 Simplifying x = 2.640096267Subproblem 2
x + -0.5625 = -2.077596267 Simplifying x + -0.5625 = -2.077596267 Reorder the terms: -0.5625 + x = -2.077596267 Solving -0.5625 + x = -2.077596267 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 = -2.077596267 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -2.077596267 + 0.5625 x = -2.077596267 + 0.5625 Combine like terms: -2.077596267 + 0.5625 = -1.515096267 x = -1.515096267 Simplifying x = -1.515096267Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.640096267, -1.515096267}
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