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Simplifying 20x2 + -48 = 100x Reorder the terms: -48 + 20x2 = 100x Solving -48 + 20x2 = 100x Solving for variable 'x'. Reorder the terms: -48 + -100x + 20x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -48 + -100x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -25x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + -25x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + -25x + 5x2 = 0 Solving -12 + -25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -5x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -5x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -5x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -5x + x2 = 0 + 2.4 -5x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -5x + x2 = 2.4 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.4 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.4 + 6.25 Combine like terms: 2.4 + 6.25 = 8.65 6.25 + -5x + x2 = 8.65 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.65 Calculate the square root of the right side: 2.941088234 Break this problem into two subproblems by setting (x + -2.5) equal to 2.941088234 and -2.941088234.Subproblem 1
x + -2.5 = 2.941088234 Simplifying x + -2.5 = 2.941088234 Reorder the terms: -2.5 + x = 2.941088234 Solving -2.5 + x = 2.941088234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.941088234 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.941088234 + 2.5 x = 2.941088234 + 2.5 Combine like terms: 2.941088234 + 2.5 = 5.441088234 x = 5.441088234 Simplifying x = 5.441088234Subproblem 2
x + -2.5 = -2.941088234 Simplifying x + -2.5 = -2.941088234 Reorder the terms: -2.5 + x = -2.941088234 Solving -2.5 + x = -2.941088234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.941088234 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.941088234 + 2.5 x = -2.941088234 + 2.5 Combine like terms: -2.941088234 + 2.5 = -0.441088234 x = -0.441088234 Simplifying x = -0.441088234Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.441088234, -0.441088234}Solution
x = {5.441088234, -0.441088234}
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