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Simplifying 2x2 + -20x + -19 = 0 Reorder the terms: -19 + -20x + 2x2 = 0 Solving -19 + -20x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + -10x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + -10x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + -10x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + -10x + x2 = 0 + 9.5 -10x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 -10x + x2 = 9.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 9.5 + 25 Reorder the terms: 25 + -10x + x2 = 9.5 + 25 Combine like terms: 9.5 + 25 = 34.5 25 + -10x + x2 = 34.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 34.5 Calculate the square root of the right side: 5.873670062 Break this problem into two subproblems by setting (x + -5) equal to 5.873670062 and -5.873670062.Subproblem 1
x + -5 = 5.873670062 Simplifying x + -5 = 5.873670062 Reorder the terms: -5 + x = 5.873670062 Solving -5 + x = 5.873670062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.873670062 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.873670062 + 5 x = 5.873670062 + 5 Combine like terms: 5.873670062 + 5 = 10.873670062 x = 10.873670062 Simplifying x = 10.873670062Subproblem 2
x + -5 = -5.873670062 Simplifying x + -5 = -5.873670062 Reorder the terms: -5 + x = -5.873670062 Solving -5 + x = -5.873670062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.873670062 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.873670062 + 5 x = -5.873670062 + 5 Combine like terms: -5.873670062 + 5 = -0.873670062 x = -0.873670062 Simplifying x = -0.873670062Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.873670062, -0.873670062}
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