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Simplifying 48x2 + 24 = 600x Reorder the terms: 24 + 48x2 = 600x Solving 24 + 48x2 = 600x Solving for variable 'x'. Reorder the terms: 24 + -600x + 48x2 = 600x + -600x Combine like terms: 600x + -600x = 0 24 + -600x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '24'. 24(1 + -25x + 2x2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(1 + -25x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -25x + 2x2 = 0 Solving 1 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -12.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -12.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -12.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -12.5x + x2 = 0 + -0.5 -12.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -12.5x + x2 = -0.5 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 = -0.5 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -0.5 + 39.0625 Combine like terms: -0.5 + 39.0625 = 38.5625 39.0625 + -12.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + -6.25) equal to 6.209871174 and -6.209871174.Subproblem 1
x + -6.25 = 6.209871174 Simplifying x + -6.25 = 6.209871174 Reorder the terms: -6.25 + x = 6.209871174 Solving -6.25 + x = 6.209871174 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 = 6.209871174 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.209871174 + 6.25 x = 6.209871174 + 6.25 Combine like terms: 6.209871174 + 6.25 = 12.459871174 x = 12.459871174 Simplifying x = 12.459871174Subproblem 2
x + -6.25 = -6.209871174 Simplifying x + -6.25 = -6.209871174 Reorder the terms: -6.25 + x = -6.209871174 Solving -6.25 + x = -6.209871174 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 = -6.209871174 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.209871174 + 6.25 x = -6.209871174 + 6.25 Combine like terms: -6.209871174 + 6.25 = 0.040128826 x = 0.040128826 Simplifying x = 0.040128826Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.459871174, 0.040128826}Solution
x = {12.459871174, 0.040128826}
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