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Simplifying 16x2 + -96x = 108 Reorder the terms: -96x + 16x2 = 108 Solving -96x + 16x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -96x + 16x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -24x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-27 + -24x + 4x2)' equal to zero and attempt to solve: Simplifying -27 + -24x + 4x2 = 0 Solving -27 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -6x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -6x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -6x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -6x + x2 = 0 + 6.75 -6x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -6x + x2 = 6.75 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 = 6.75 + 9 Reorder the terms: 9 + -6x + x2 = 6.75 + 9 Combine like terms: 6.75 + 9 = 15.75 9 + -6x + x2 = 15.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 15.75 Calculate the square root of the right side: 3.968626967 Break this problem into two subproblems by setting (x + -3) equal to 3.968626967 and -3.968626967.Subproblem 1
x + -3 = 3.968626967 Simplifying x + -3 = 3.968626967 Reorder the terms: -3 + x = 3.968626967 Solving -3 + x = 3.968626967 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 = 3.968626967 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.968626967 + 3 x = 3.968626967 + 3 Combine like terms: 3.968626967 + 3 = 6.968626967 x = 6.968626967 Simplifying x = 6.968626967Subproblem 2
x + -3 = -3.968626967 Simplifying x + -3 = -3.968626967 Reorder the terms: -3 + x = -3.968626967 Solving -3 + x = -3.968626967 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 = -3.968626967 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.968626967 + 3 x = -3.968626967 + 3 Combine like terms: -3.968626967 + 3 = -0.968626967 x = -0.968626967 Simplifying x = -0.968626967Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.968626967, -0.968626967}Solution
x = {6.968626967, -0.968626967}
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