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Simplifying 4x2 + -2x + 24 = 600 Reorder the terms: 24 + -2x + 4x2 = 600 Solving 24 + -2x + 4x2 = 600 Solving for variable 'x'. Reorder the terms: 24 + -600 + -2x + 4x2 = 600 + -600 Combine like terms: 24 + -600 = -576 -576 + -2x + 4x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -576 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-288 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-288 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -288 + -1x + 2x2 = 0 Solving -288 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -144 + -0.5x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + -0.5x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -0.5x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -0.5x + x2 = 0 + 144 -0.5x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -0.5x + x2 = 144 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 144 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 144 + 0.0625 Combine like terms: 144 + 0.0625 = 144.0625 0.0625 + -0.5x + x2 = 144.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 144.0625 Calculate the square root of the right side: 12.002603884 Break this problem into two subproblems by setting (x + -0.25) equal to 12.002603884 and -12.002603884.Subproblem 1
x + -0.25 = 12.002603884 Simplifying x + -0.25 = 12.002603884 Reorder the terms: -0.25 + x = 12.002603884 Solving -0.25 + x = 12.002603884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 12.002603884 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 12.002603884 + 0.25 x = 12.002603884 + 0.25 Combine like terms: 12.002603884 + 0.25 = 12.252603884 x = 12.252603884 Simplifying x = 12.252603884Subproblem 2
x + -0.25 = -12.002603884 Simplifying x + -0.25 = -12.002603884 Reorder the terms: -0.25 + x = -12.002603884 Solving -0.25 + x = -12.002603884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -12.002603884 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -12.002603884 + 0.25 x = -12.002603884 + 0.25 Combine like terms: -12.002603884 + 0.25 = -11.752603884 x = -11.752603884 Simplifying x = -11.752603884Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.252603884, -11.752603884}Solution
x = {12.252603884, -11.752603884}
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