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Simplifying 4x2 = 50x + -120 Reorder the terms: 4x2 = -120 + 50x Solving 4x2 = -120 + 50x Solving for variable 'x'. Reorder the terms: 120 + -50x + 4x2 = -120 + 50x + 120 + -50x Reorder the terms: 120 + -50x + 4x2 = -120 + 120 + 50x + -50x Combine like terms: -120 + 120 = 0 120 + -50x + 4x2 = 0 + 50x + -50x 120 + -50x + 4x2 = 50x + -50x Combine like terms: 50x + -50x = 0 120 + -50x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -25x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -25x + 2x2)' equal to zero and attempt to solve: Simplifying 60 + -25x + 2x2 = 0 Solving 60 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 30 + -12.5x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12.5x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -12.5x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12.5x + x2 = 0 + -30 -12.5x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12.5x + x2 = -30 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -30 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -30 + 39.0625 Combine like terms: -30 + 39.0625 = 9.0625 39.0625 + -12.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -6.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -6.25 = 3.010398645 Simplifying x + -6.25 = 3.010398645 Reorder the terms: -6.25 + x = 3.010398645 Solving -6.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 3.010398645 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 3.010398645 + 6.25 x = 3.010398645 + 6.25 Combine like terms: 3.010398645 + 6.25 = 9.260398645 x = 9.260398645 Simplifying x = 9.260398645Subproblem 2
x + -6.25 = -3.010398645 Simplifying x + -6.25 = -3.010398645 Reorder the terms: -6.25 + x = -3.010398645 Solving -6.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -3.010398645 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -3.010398645 + 6.25 x = -3.010398645 + 6.25 Combine like terms: -3.010398645 + 6.25 = 3.239601355 x = 3.239601355 Simplifying x = 3.239601355Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.260398645, 3.239601355}Solution
x = {9.260398645, 3.239601355}
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