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Simplifying 600 = 2x2 + 10x + -48 Reorder the terms: 600 = -48 + 10x + 2x2 Solving 600 = -48 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 600 + 48 = 648 648 + -10x + -2x2 = -48 + 10x + 2x2 + 48 + -10x + -2x2 Reorder the terms: 648 + -10x + -2x2 = -48 + 48 + 10x + -10x + 2x2 + -2x2 Combine like terms: -48 + 48 = 0 648 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 648 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 648 + -10x + -2x2 = 0 + 2x2 + -2x2 648 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 648 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(324 + -5x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(324 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 324 + -5x + -1x2 = 0 Solving 324 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -324 + 5x + x2 = 0 Move the constant term to the right: Add '324' to each side of the equation. -324 + 5x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 5x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 5x + x2 = 0 + 324 5x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 5x + x2 = 324 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 324 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 324 + 6.25 Combine like terms: 324 + 6.25 = 330.25 6.25 + 5x + x2 = 330.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 330.25 Calculate the square root of the right side: 18.172781845 Break this problem into two subproblems by setting (x + 2.5) equal to 18.172781845 and -18.172781845.Subproblem 1
x + 2.5 = 18.172781845 Simplifying x + 2.5 = 18.172781845 Reorder the terms: 2.5 + x = 18.172781845 Solving 2.5 + x = 18.172781845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 18.172781845 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 18.172781845 + -2.5 x = 18.172781845 + -2.5 Combine like terms: 18.172781845 + -2.5 = 15.672781845 x = 15.672781845 Simplifying x = 15.672781845Subproblem 2
x + 2.5 = -18.172781845 Simplifying x + 2.5 = -18.172781845 Reorder the terms: 2.5 + x = -18.172781845 Solving 2.5 + x = -18.172781845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -18.172781845 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -18.172781845 + -2.5 x = -18.172781845 + -2.5 Combine like terms: -18.172781845 + -2.5 = -20.672781845 x = -20.672781845 Simplifying x = -20.672781845Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.672781845, -20.672781845}Solution
x = {15.672781845, -20.672781845}
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