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Simplifying 2x2 + 48x + -900 = 0 Reorder the terms: -900 + 48x + 2x2 = 0 Solving -900 + 48x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-450 + 24x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-450 + 24x + x2)' equal to zero and attempt to solve: Simplifying -450 + 24x + x2 = 0 Solving -450 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 24x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 24x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 24x + x2 = 0 + 450 24x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 24x + x2 = 450 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 = 450 + 144 Reorder the terms: 144 + 24x + x2 = 450 + 144 Combine like terms: 450 + 144 = 594 144 + 24x + x2 = 594 Factor a perfect square on the left side: (x + 12)(x + 12) = 594 Calculate the square root of the right side: 24.372115214 Break this problem into two subproblems by setting (x + 12) equal to 24.372115214 and -24.372115214.Subproblem 1
x + 12 = 24.372115214 Simplifying x + 12 = 24.372115214 Reorder the terms: 12 + x = 24.372115214 Solving 12 + x = 24.372115214 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 = 24.372115214 + -12 Combine like terms: 12 + -12 = 0 0 + x = 24.372115214 + -12 x = 24.372115214 + -12 Combine like terms: 24.372115214 + -12 = 12.372115214 x = 12.372115214 Simplifying x = 12.372115214Subproblem 2
x + 12 = -24.372115214 Simplifying x + 12 = -24.372115214 Reorder the terms: 12 + x = -24.372115214 Solving 12 + x = -24.372115214 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 = -24.372115214 + -12 Combine like terms: 12 + -12 = 0 0 + x = -24.372115214 + -12 x = -24.372115214 + -12 Combine like terms: -24.372115214 + -12 = -36.372115214 x = -36.372115214 Simplifying x = -36.372115214Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.372115214, -36.372115214}Solution
x = {12.372115214, -36.372115214}
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