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Simplifying 24x * x + 240x = 48 Multiply x * x 24x2 + 240x = 48 Reorder the terms: 240x + 24x2 = 48 Solving 240x + 24x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 240x + 24x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 240x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '24'. 24(-2 + 10x + x2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(-2 + 10x + x2)' equal to zero and attempt to solve: Simplifying -2 + 10x + x2 = 0 Solving -2 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 10x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 10x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 10x + x2 = 0 + 2 10x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 10x + x2 = 2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 2 + 25 Reorder the terms: 25 + 10x + x2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + 10x + x2 = 27 Factor a perfect square on the left side: (x + 5)(x + 5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 5) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 5 = 5.196152423 Simplifying x + 5 = 5.196152423 Reorder the terms: 5 + x = 5.196152423 Solving 5 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.196152423 + -5 x = 5.196152423 + -5 Combine like terms: 5.196152423 + -5 = 0.196152423 x = 0.196152423 Simplifying x = 0.196152423Subproblem 2
x + 5 = -5.196152423 Simplifying x + 5 = -5.196152423 Reorder the terms: 5 + x = -5.196152423 Solving 5 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.196152423 + -5 x = -5.196152423 + -5 Combine like terms: -5.196152423 + -5 = -10.196152423 x = -10.196152423 Simplifying x = -10.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196152423, -10.196152423}Solution
x = {0.196152423, -10.196152423}
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