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Simplifying 0 = -16x2 + 92x + 48 Reorder the terms: 0 = 48 + 92x + -16x2 Solving 0 = 48 + 92x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -48 = -48 -48 + -92x + 16x2 = 48 + 92x + -16x2 + -48 + -92x + 16x2 Reorder the terms: -48 + -92x + 16x2 = 48 + -48 + 92x + -92x + -16x2 + 16x2 Combine like terms: 48 + -48 = 0 -48 + -92x + 16x2 = 0 + 92x + -92x + -16x2 + 16x2 -48 + -92x + 16x2 = 92x + -92x + -16x2 + 16x2 Combine like terms: 92x + -92x = 0 -48 + -92x + 16x2 = 0 + -16x2 + 16x2 -48 + -92x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -48 + -92x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -23x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + -23x + 4x2)' equal to zero and attempt to solve: Simplifying -12 + -23x + 4x2 = 0 Solving -12 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + -5.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.75x + x2 = 0 + 3 -5.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.75x + x2 = 3 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 3 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 3 + 8.265625 Combine like terms: 3 + 8.265625 = 11.265625 8.265625 + -5.75x + x2 = 11.265625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (x + -2.875) equal to 3.356430396 and -3.356430396.Subproblem 1
x + -2.875 = 3.356430396 Simplifying x + -2.875 = 3.356430396 Reorder the terms: -2.875 + x = 3.356430396 Solving -2.875 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.356430396 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.356430396 + 2.875 x = 3.356430396 + 2.875 Combine like terms: 3.356430396 + 2.875 = 6.231430396 x = 6.231430396 Simplifying x = 6.231430396Subproblem 2
x + -2.875 = -3.356430396 Simplifying x + -2.875 = -3.356430396 Reorder the terms: -2.875 + x = -3.356430396 Solving -2.875 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.356430396 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.356430396 + 2.875 x = -3.356430396 + 2.875 Combine like terms: -3.356430396 + 2.875 = -0.481430396 x = -0.481430396 Simplifying x = -0.481430396Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.231430396, -0.481430396}Solution
x = {6.231430396, -0.481430396}
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