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Simplifying 4x2 + 96x + -1092 = 0 Reorder the terms: -1092 + 96x + 4x2 = 0 Solving -1092 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-273 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-273 + 24x + x2)' equal to zero and attempt to solve: Simplifying -273 + 24x + x2 = 0 Solving -273 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '273' to each side of the equation. -273 + 24x + 273 + x2 = 0 + 273 Reorder the terms: -273 + 273 + 24x + x2 = 0 + 273 Combine like terms: -273 + 273 = 0 0 + 24x + x2 = 0 + 273 24x + x2 = 0 + 273 Combine like terms: 0 + 273 = 273 24x + x2 = 273 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 = 273 + 144 Reorder the terms: 144 + 24x + x2 = 273 + 144 Combine like terms: 273 + 144 = 417 144 + 24x + x2 = 417 Factor a perfect square on the left side: (x + 12)(x + 12) = 417 Calculate the square root of the right side: 20.420577857 Break this problem into two subproblems by setting (x + 12) equal to 20.420577857 and -20.420577857.Subproblem 1
x + 12 = 20.420577857 Simplifying x + 12 = 20.420577857 Reorder the terms: 12 + x = 20.420577857 Solving 12 + x = 20.420577857 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 = 20.420577857 + -12 Combine like terms: 12 + -12 = 0 0 + x = 20.420577857 + -12 x = 20.420577857 + -12 Combine like terms: 20.420577857 + -12 = 8.420577857 x = 8.420577857 Simplifying x = 8.420577857Subproblem 2
x + 12 = -20.420577857 Simplifying x + 12 = -20.420577857 Reorder the terms: 12 + x = -20.420577857 Solving 12 + x = -20.420577857 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 = -20.420577857 + -12 Combine like terms: 12 + -12 = 0 0 + x = -20.420577857 + -12 x = -20.420577857 + -12 Combine like terms: -20.420577857 + -12 = -32.420577857 x = -32.420577857 Simplifying x = -32.420577857Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.420577857, -32.420577857}Solution
x = {8.420577857, -32.420577857}
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