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Simplifying 20x2 + -100x + -1900 = 0 Reorder the terms: -1900 + -100x + 20x2 = 0 Solving -1900 + -100x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20'. 20(-95 + -5x + x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-95 + -5x + x2)' equal to zero and attempt to solve: Simplifying -95 + -5x + x2 = 0 Solving -95 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -5x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + -5x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -5x + x2 = 0 + 95 -5x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 -5x + x2 = 95 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 = 95 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 95 + 6.25 Combine like terms: 95 + 6.25 = 101.25 6.25 + -5x + x2 = 101.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + -2.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + -2.5 = 10.062305899 Simplifying x + -2.5 = 10.062305899 Reorder the terms: -2.5 + x = 10.062305899 Solving -2.5 + x = 10.062305899 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 = 10.062305899 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.062305899 + 2.5 x = 10.062305899 + 2.5 Combine like terms: 10.062305899 + 2.5 = 12.562305899 x = 12.562305899 Simplifying x = 12.562305899Subproblem 2
x + -2.5 = -10.062305899 Simplifying x + -2.5 = -10.062305899 Reorder the terms: -2.5 + x = -10.062305899 Solving -2.5 + x = -10.062305899 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 = -10.062305899 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.062305899 + 2.5 x = -10.062305899 + 2.5 Combine like terms: -10.062305899 + 2.5 = -7.562305899 x = -7.562305899 Simplifying x = -7.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.562305899, -7.562305899}Solution
x = {12.562305899, -7.562305899}
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