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Simplifying -16x2 + 96x + -28 = 0 Reorder the terms: -28 + 96x + -16x2 = 0 Solving -28 + 96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 24x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 24x + -4x2)' equal to zero and attempt to solve: Simplifying -7 + 24x + -4x2 = 0 Solving -7 + 24x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.75 + -6x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -6x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -6x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -6x + x2 = 0 + -1.75 -6x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -6x + x2 = -1.75 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.75 + 9 Reorder the terms: 9 + -6x + x2 = -1.75 + 9 Combine like terms: -1.75 + 9 = 7.25 9 + -6x + x2 = 7.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -3) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -3 = 2.692582404 Simplifying x + -3 = 2.692582404 Reorder the terms: -3 + x = 2.692582404 Solving -3 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.692582404 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.692582404 + 3 x = 2.692582404 + 3 Combine like terms: 2.692582404 + 3 = 5.692582404 x = 5.692582404 Simplifying x = 5.692582404Subproblem 2
x + -3 = -2.692582404 Simplifying x + -3 = -2.692582404 Reorder the terms: -3 + x = -2.692582404 Solving -3 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.692582404 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.692582404 + 3 x = -2.692582404 + 3 Combine like terms: -2.692582404 + 3 = 0.307417596 x = 0.307417596 Simplifying x = 0.307417596Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.692582404, 0.307417596}Solution
x = {5.692582404, 0.307417596}
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