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Simplifying 12x2 + -300x + 1350 = 0 Reorder the terms: 1350 + -300x + 12x2 = 0 Solving 1350 + -300x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(225 + -50x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(225 + -50x + 2x2)' equal to zero and attempt to solve: Simplifying 225 + -50x + 2x2 = 0 Solving 225 + -50x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 112.5 + -25x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -25x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -25x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -25x + x2 = 0 + -112.5 -25x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -25x + x2 = -112.5 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -112.5 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -112.5 + 156.25 Combine like terms: -112.5 + 156.25 = 43.75 156.25 + -25x + x2 = 43.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (x + -12.5) equal to 6.614378278 and -6.614378278.Subproblem 1
x + -12.5 = 6.614378278 Simplifying x + -12.5 = 6.614378278 Reorder the terms: -12.5 + x = 6.614378278 Solving -12.5 + x = 6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 6.614378278 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 6.614378278 + 12.5 x = 6.614378278 + 12.5 Combine like terms: 6.614378278 + 12.5 = 19.114378278 x = 19.114378278 Simplifying x = 19.114378278Subproblem 2
x + -12.5 = -6.614378278 Simplifying x + -12.5 = -6.614378278 Reorder the terms: -12.5 + x = -6.614378278 Solving -12.5 + x = -6.614378278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -6.614378278 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -6.614378278 + 12.5 x = -6.614378278 + 12.5 Combine like terms: -6.614378278 + 12.5 = 5.885621722 x = 5.885621722 Simplifying x = 5.885621722Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.114378278, 5.885621722}Solution
x = {19.114378278, 5.885621722}
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