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Simplifying 4x2 + -16x = 2304 Reorder the terms: -16x + 4x2 = 2304 Solving -16x + 4x2 = 2304 Solving for variable 'x'. Reorder the terms: -2304 + -16x + 4x2 = 2304 + -2304 Combine like terms: 2304 + -2304 = 0 -2304 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-576 + -4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-576 + -4x + x2)' equal to zero and attempt to solve: Simplifying -576 + -4x + x2 = 0 Solving -576 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + -4x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + -4x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + -4x + x2 = 0 + 576 -4x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 -4x + x2 = 576 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 576 + 4 Reorder the terms: 4 + -4x + x2 = 576 + 4 Combine like terms: 576 + 4 = 580 4 + -4x + x2 = 580 Factor a perfect square on the left side: (x + -2)(x + -2) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (x + -2) equal to 24.083189158 and -24.083189158.Subproblem 1
x + -2 = 24.083189158 Simplifying x + -2 = 24.083189158 Reorder the terms: -2 + x = 24.083189158 Solving -2 + x = 24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 24.083189158 + 2 Combine like terms: -2 + 2 = 0 0 + x = 24.083189158 + 2 x = 24.083189158 + 2 Combine like terms: 24.083189158 + 2 = 26.083189158 x = 26.083189158 Simplifying x = 26.083189158Subproblem 2
x + -2 = -24.083189158 Simplifying x + -2 = -24.083189158 Reorder the terms: -2 + x = -24.083189158 Solving -2 + x = -24.083189158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -24.083189158 + 2 Combine like terms: -2 + 2 = 0 0 + x = -24.083189158 + 2 x = -24.083189158 + 2 Combine like terms: -24.083189158 + 2 = -22.083189158 x = -22.083189158 Simplifying x = -22.083189158Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.083189158, -22.083189158}Solution
x = {26.083189158, -22.083189158}
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