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Simplifying 3x2 + 72x = 240 Reorder the terms: 72x + 3x2 = 240 Solving 72x + 3x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 72x + 3x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 72x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-80 + 24x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-80 + 24x + x2)' equal to zero and attempt to solve: Simplifying -80 + 24x + x2 = 0 Solving -80 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 24x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 24x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 24x + x2 = 0 + 80 24x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 24x + x2 = 80 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 = 80 + 144 Reorder the terms: 144 + 24x + x2 = 80 + 144 Combine like terms: 80 + 144 = 224 144 + 24x + x2 = 224 Factor a perfect square on the left side: (x + 12)(x + 12) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + 12) equal to 14.966629547 and -14.966629547.Subproblem 1
x + 12 = 14.966629547 Simplifying x + 12 = 14.966629547 Reorder the terms: 12 + x = 14.966629547 Solving 12 + x = 14.966629547 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 = 14.966629547 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.966629547 + -12 x = 14.966629547 + -12 Combine like terms: 14.966629547 + -12 = 2.966629547 x = 2.966629547 Simplifying x = 2.966629547Subproblem 2
x + 12 = -14.966629547 Simplifying x + 12 = -14.966629547 Reorder the terms: 12 + x = -14.966629547 Solving 12 + x = -14.966629547 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 = -14.966629547 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.966629547 + -12 x = -14.966629547 + -12 Combine like terms: -14.966629547 + -12 = -26.966629547 x = -26.966629547 Simplifying x = -26.966629547Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.966629547, -26.966629547}Solution
x = {2.966629547, -26.966629547}
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