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Simplifying 12x2 + 180x + -600 = 0 Reorder the terms: -600 + 180x + 12x2 = 0 Solving -600 + 180x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-50 + 15x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-50 + 15x + x2)' equal to zero and attempt to solve: Simplifying -50 + 15x + x2 = 0 Solving -50 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 15x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 15x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 15x + x2 = 0 + 50 15x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 15x + x2 = 50 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 50 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + 15x + x2 = 106.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + 7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + 7.5 = 10.307764064 Simplifying x + 7.5 = 10.307764064 Reorder the terms: 7.5 + x = 10.307764064 Solving 7.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.307764064 + -7.5 x = 10.307764064 + -7.5 Combine like terms: 10.307764064 + -7.5 = 2.807764064 x = 2.807764064 Simplifying x = 2.807764064Subproblem 2
x + 7.5 = -10.307764064 Simplifying x + 7.5 = -10.307764064 Reorder the terms: 7.5 + x = -10.307764064 Solving 7.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.307764064 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.307764064 + -7.5 x = -10.307764064 + -7.5 Combine like terms: -10.307764064 + -7.5 = -17.807764064 x = -17.807764064 Simplifying x = -17.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.807764064, -17.807764064}Solution
x = {2.807764064, -17.807764064}
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