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Simplifying -16x2 + 192x + 4 = 0 Reorder the terms: 4 + 192x + -16x2 = 0 Solving 4 + 192x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 48x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 48x + -4x2)' equal to zero and attempt to solve: Simplifying 1 + 48x + -4x2 = 0 Solving 1 + 48x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -12x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -12x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -12x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -12x + x2 = 0 + 0.25 -12x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -12x + x2 = 0.25 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 0.25 + 36 Reorder the terms: 36 + -12x + x2 = 0.25 + 36 Combine like terms: 0.25 + 36 = 36.25 36 + -12x + x2 = 36.25 Factor a perfect square on the left side: (x + -6)(x + -6) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + -6) equal to 6.020797289 and -6.020797289.Subproblem 1
x + -6 = 6.020797289 Simplifying x + -6 = 6.020797289 Reorder the terms: -6 + x = 6.020797289 Solving -6 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.020797289 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.020797289 + 6 x = 6.020797289 + 6 Combine like terms: 6.020797289 + 6 = 12.020797289 x = 12.020797289 Simplifying x = 12.020797289Subproblem 2
x + -6 = -6.020797289 Simplifying x + -6 = -6.020797289 Reorder the terms: -6 + x = -6.020797289 Solving -6 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.020797289 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.020797289 + 6 x = -6.020797289 + 6 Combine like terms: -6.020797289 + 6 = -0.020797289 x = -0.020797289 Simplifying x = -0.020797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.020797289, -0.020797289}Solution
x = {12.020797289, -0.020797289}
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