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Simplifying 0 = -16X2 + 18X + 112 Reorder the terms: 0 = 112 + 18X + -16X2 Solving 0 = 112 + 18X + -16X2 Solving for variable 'X'. Combine like terms: 0 + -112 = -112 -112 + -18X + 16X2 = 112 + 18X + -16X2 + -112 + -18X + 16X2 Reorder the terms: -112 + -18X + 16X2 = 112 + -112 + 18X + -18X + -16X2 + 16X2 Combine like terms: 112 + -112 = 0 -112 + -18X + 16X2 = 0 + 18X + -18X + -16X2 + 16X2 -112 + -18X + 16X2 = 18X + -18X + -16X2 + 16X2 Combine like terms: 18X + -18X = 0 -112 + -18X + 16X2 = 0 + -16X2 + 16X2 -112 + -18X + 16X2 = -16X2 + 16X2 Combine like terms: -16X2 + 16X2 = 0 -112 + -18X + 16X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + -9X + 8X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-56 + -9X + 8X2)' equal to zero and attempt to solve: Simplifying -56 + -9X + 8X2 = 0 Solving -56 + -9X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7 + -1.125X + X2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -1.125X + 7 + X2 = 0 + 7 Reorder the terms: -7 + 7 + -1.125X + X2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1.125X + X2 = 0 + 7 -1.125X + X2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1.125X + X2 = 7 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 = 7 + 0.31640625 Reorder the terms: 0.31640625 + -1.125X + X2 = 7 + 0.31640625 Combine like terms: 7 + 0.31640625 = 7.31640625 0.31640625 + -1.125X + X2 = 7.31640625 Factor a perfect square on the left side: (X + -0.5625)(X + -0.5625) = 7.31640625 Calculate the square root of the right side: 2.704885626 Break this problem into two subproblems by setting (X + -0.5625) equal to 2.704885626 and -2.704885626.Subproblem 1
X + -0.5625 = 2.704885626 Simplifying X + -0.5625 = 2.704885626 Reorder the terms: -0.5625 + X = 2.704885626 Solving -0.5625 + X = 2.704885626 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 = 2.704885626 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + X = 2.704885626 + 0.5625 X = 2.704885626 + 0.5625 Combine like terms: 2.704885626 + 0.5625 = 3.267385626 X = 3.267385626 Simplifying X = 3.267385626Subproblem 2
X + -0.5625 = -2.704885626 Simplifying X + -0.5625 = -2.704885626 Reorder the terms: -0.5625 + X = -2.704885626 Solving -0.5625 + X = -2.704885626 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 = -2.704885626 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + X = -2.704885626 + 0.5625 X = -2.704885626 + 0.5625 Combine like terms: -2.704885626 + 0.5625 = -2.142385626 X = -2.142385626 Simplifying X = -2.142385626Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.267385626, -2.142385626}Solution
X = {3.267385626, -2.142385626}
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