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Simplifying 4x2 + 96x + -288 = 0 Reorder the terms: -288 + 96x + 4x2 = 0 Solving -288 + 96x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-72 + 24x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-72 + 24x + x2)' equal to zero and attempt to solve: Simplifying -72 + 24x + x2 = 0 Solving -72 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 24x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 24x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 24x + x2 = 0 + 72 24x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 24x + x2 = 72 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 = 72 + 144 Reorder the terms: 144 + 24x + x2 = 72 + 144 Combine like terms: 72 + 144 = 216 144 + 24x + x2 = 216 Factor a perfect square on the left side: (x + 12)(x + 12) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 12) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 12 = 14.696938457 Simplifying x + 12 = 14.696938457 Reorder the terms: 12 + x = 14.696938457 Solving 12 + x = 14.696938457 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 = 14.696938457 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.696938457 + -12 x = 14.696938457 + -12 Combine like terms: 14.696938457 + -12 = 2.696938457 x = 2.696938457 Simplifying x = 2.696938457Subproblem 2
x + 12 = -14.696938457 Simplifying x + 12 = -14.696938457 Reorder the terms: 12 + x = -14.696938457 Solving 12 + x = -14.696938457 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 = -14.696938457 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.696938457 + -12 x = -14.696938457 + -12 Combine like terms: -14.696938457 + -12 = -26.696938457 x = -26.696938457 Simplifying x = -26.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.696938457, -26.696938457}Solution
x = {2.696938457, -26.696938457}
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