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Simplifying 5x2 + -95x + -20 = 0 Reorder the terms: -20 + -95x + 5x2 = 0 Solving -20 + -95x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -19x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -19x + x2)' equal to zero and attempt to solve: Simplifying -4 + -19x + x2 = 0 Solving -4 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -19x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -19x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -19x + x2 = 0 + 4 -19x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -19x + x2 = 4 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 4 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 4 + 90.25 Combine like terms: 4 + 90.25 = 94.25 90.25 + -19x + x2 = 94.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + -9.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + -9.5 = 9.708243919 Simplifying x + -9.5 = 9.708243919 Reorder the terms: -9.5 + x = 9.708243919 Solving -9.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.708243919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.708243919 + 9.5 x = 9.708243919 + 9.5 Combine like terms: 9.708243919 + 9.5 = 19.208243919 x = 19.208243919 Simplifying x = 19.208243919Subproblem 2
x + -9.5 = -9.708243919 Simplifying x + -9.5 = -9.708243919 Reorder the terms: -9.5 + x = -9.708243919 Solving -9.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.708243919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.708243919 + 9.5 x = -9.708243919 + 9.5 Combine like terms: -9.708243919 + 9.5 = -0.208243919 x = -0.208243919 Simplifying x = -0.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.208243919, -0.208243919}Solution
x = {19.208243919, -0.208243919}
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