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Simplifying 3900 = 5x2 + -120x + 3300 Reorder the terms: 3900 = 3300 + -120x + 5x2 Solving 3900 = 3300 + -120x + 5x2 Solving for variable 'x'. Combine like terms: 3900 + -3300 = 600 600 + 120x + -5x2 = 3300 + -120x + 5x2 + -3300 + 120x + -5x2 Reorder the terms: 600 + 120x + -5x2 = 3300 + -3300 + -120x + 120x + 5x2 + -5x2 Combine like terms: 3300 + -3300 = 0 600 + 120x + -5x2 = 0 + -120x + 120x + 5x2 + -5x2 600 + 120x + -5x2 = -120x + 120x + 5x2 + -5x2 Combine like terms: -120x + 120x = 0 600 + 120x + -5x2 = 0 + 5x2 + -5x2 600 + 120x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 600 + 120x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(120 + 24x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(120 + 24x + -1x2)' equal to zero and attempt to solve: Simplifying 120 + 24x + -1x2 = 0 Solving 120 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -120 + -24x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -24x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -24x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -24x + x2 = 0 + 120 -24x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -24x + x2 = 120 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 = 120 + 144 Reorder the terms: 144 + -24x + x2 = 120 + 144 Combine like terms: 120 + 144 = 264 144 + -24x + x2 = 264 Factor a perfect square on the left side: (x + -12)(x + -12) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x + -12) equal to 16.248076809 and -16.248076809.Subproblem 1
x + -12 = 16.248076809 Simplifying x + -12 = 16.248076809 Reorder the terms: -12 + x = 16.248076809 Solving -12 + x = 16.248076809 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 = 16.248076809 + 12 Combine like terms: -12 + 12 = 0 0 + x = 16.248076809 + 12 x = 16.248076809 + 12 Combine like terms: 16.248076809 + 12 = 28.248076809 x = 28.248076809 Simplifying x = 28.248076809Subproblem 2
x + -12 = -16.248076809 Simplifying x + -12 = -16.248076809 Reorder the terms: -12 + x = -16.248076809 Solving -12 + x = -16.248076809 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 = -16.248076809 + 12 Combine like terms: -12 + 12 = 0 0 + x = -16.248076809 + 12 x = -16.248076809 + 12 Combine like terms: -16.248076809 + 12 = -4.248076809 x = -4.248076809 Simplifying x = -4.248076809Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.248076809, -4.248076809}Solution
x = {28.248076809, -4.248076809}
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