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Simplifying 4x2 + 96x + -768 = 0 Reorder the terms: -768 + 96x + 4x2 = 0 Solving -768 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-192 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-192 + 24x + x2)' equal to zero and attempt to solve: Simplifying -192 + 24x + x2 = 0 Solving -192 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 24x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 24x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 24x + x2 = 0 + 192 24x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 24x + x2 = 192 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 = 192 + 144 Reorder the terms: 144 + 24x + x2 = 192 + 144 Combine like terms: 192 + 144 = 336 144 + 24x + x2 = 336 Factor a perfect square on the left side: (x + 12)(x + 12) = 336 Calculate the square root of the right side: 18.33030278 Break this problem into two subproblems by setting (x + 12) equal to 18.33030278 and -18.33030278.Subproblem 1
x + 12 = 18.33030278 Simplifying x + 12 = 18.33030278 Reorder the terms: 12 + x = 18.33030278 Solving 12 + x = 18.33030278 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 = 18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + x = 18.33030278 + -12 x = 18.33030278 + -12 Combine like terms: 18.33030278 + -12 = 6.33030278 x = 6.33030278 Simplifying x = 6.33030278Subproblem 2
x + 12 = -18.33030278 Simplifying x + 12 = -18.33030278 Reorder the terms: 12 + x = -18.33030278 Solving 12 + x = -18.33030278 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 = -18.33030278 + -12 Combine like terms: 12 + -12 = 0 0 + x = -18.33030278 + -12 x = -18.33030278 + -12 Combine like terms: -18.33030278 + -12 = -30.33030278 x = -30.33030278 Simplifying x = -30.33030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.33030278, -30.33030278}Solution
x = {6.33030278, -30.33030278}
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