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Simplifying 0 = -16x2 + 16x + 112 Reorder the terms: 0 = 112 + 16x + -16x2 Solving 0 = 112 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -112 = -112 -112 + -16x + 16x2 = 112 + 16x + -16x2 + -112 + -16x + 16x2 Reorder the terms: -112 + -16x + 16x2 = 112 + -112 + 16x + -16x + -16x2 + 16x2 Combine like terms: 112 + -112 = 0 -112 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 -112 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 -112 + -16x + 16x2 = 0 + -16x2 + 16x2 -112 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -112 + -16x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-7 + -1x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-7 + -1x + x2)' equal to zero and attempt to solve: Simplifying -7 + -1x + x2 = 0 Solving -7 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -1x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -1x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x + x2 = 0 + 7 -1x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1x + x2 = 7 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 7 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1x + x2 = 7.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -0.5 = 2.692582404 Simplifying x + -0.5 = 2.692582404 Reorder the terms: -0.5 + x = 2.692582404 Solving -0.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.692582404 + 0.5 x = 2.692582404 + 0.5 Combine like terms: 2.692582404 + 0.5 = 3.192582404 x = 3.192582404 Simplifying x = 3.192582404Subproblem 2
x + -0.5 = -2.692582404 Simplifying x + -0.5 = -2.692582404 Reorder the terms: -0.5 + x = -2.692582404 Solving -0.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.692582404 + 0.5 x = -2.692582404 + 0.5 Combine like terms: -2.692582404 + 0.5 = -2.192582404 x = -2.192582404 Simplifying x = -2.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.192582404, -2.192582404}Solution
x = {3.192582404, -2.192582404}
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