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Simplifying 4x2 + 96x + -88 = 0 Reorder the terms: -88 + 96x + 4x2 = 0 Solving -88 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-22 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-22 + 24x + x2)' equal to zero and attempt to solve: Simplifying -22 + 24x + x2 = 0 Solving -22 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 24x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 24x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 24x + x2 = 0 + 22 24x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 24x + x2 = 22 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 22 + 144 Reorder the terms: 144 + 24x + x2 = 22 + 144 Combine like terms: 22 + 144 = 166 144 + 24x + x2 = 166 Factor a perfect square on the left side: (x + 12)(x + 12) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 12) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 12 = 12.884098727 Simplifying x + 12 = 12.884098727 Reorder the terms: 12 + x = 12.884098727 Solving 12 + x = 12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.884098727 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.884098727 + -12 x = 12.884098727 + -12 Combine like terms: 12.884098727 + -12 = 0.884098727 x = 0.884098727 Simplifying x = 0.884098727Subproblem 2
x + 12 = -12.884098727 Simplifying x + 12 = -12.884098727 Reorder the terms: 12 + x = -12.884098727 Solving 12 + x = -12.884098727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.884098727 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.884098727 + -12 x = -12.884098727 + -12 Combine like terms: -12.884098727 + -12 = -24.884098727 x = -24.884098727 Simplifying x = -24.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.884098727, -24.884098727}Solution
x = {0.884098727, -24.884098727}
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