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Simplifying 8x2 + -9x + -112 = 0 Reorder the terms: -112 + -9x + 8x2 = 0 Solving -112 + -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'. -14 + -1.125x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -1.125x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -1.125x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1.125x + x2 = 0 + 14 -1.125x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1.125x + x2 = 14 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 = 14 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 14 + 0.31640625 Combine like terms: 14 + 0.31640625 = 14.31640625 0.31640625 + -1.125x + x2 = 14.31640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 14.31640625 Calculate the square root of the right side: 3.783702717 Break this problem into two subproblems by setting (x + -0.5625) equal to 3.783702717 and -3.783702717.Subproblem 1
x + -0.5625 = 3.783702717 Simplifying x + -0.5625 = 3.783702717 Reorder the terms: -0.5625 + x = 3.783702717 Solving -0.5625 + x = 3.783702717 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 = 3.783702717 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 3.783702717 + 0.5625 x = 3.783702717 + 0.5625 Combine like terms: 3.783702717 + 0.5625 = 4.346202717 x = 4.346202717 Simplifying x = 4.346202717Subproblem 2
x + -0.5625 = -3.783702717 Simplifying x + -0.5625 = -3.783702717 Reorder the terms: -0.5625 + x = -3.783702717 Solving -0.5625 + x = -3.783702717 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 = -3.783702717 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -3.783702717 + 0.5625 x = -3.783702717 + 0.5625 Combine like terms: -3.783702717 + 0.5625 = -3.221202717 x = -3.221202717 Simplifying x = -3.221202717Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.346202717, -3.221202717}
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