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Simplifying 2x2 + -100x + -5 = 0 Reorder the terms: -5 + -100x + 2x2 = 0 Solving -5 + -100x + 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'. -2.5 + -50x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -50x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -50x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -50x + x2 = 0 + 2.5 -50x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -50x + x2 = 2.5 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 2.5 + 625 Reorder the terms: 625 + -50x + x2 = 2.5 + 625 Combine like terms: 2.5 + 625 = 627.5 625 + -50x + x2 = 627.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 627.5 Calculate the square root of the right side: 25.0499501 Break this problem into two subproblems by setting (x + -25) equal to 25.0499501 and -25.0499501.Subproblem 1
x + -25 = 25.0499501 Simplifying x + -25 = 25.0499501 Reorder the terms: -25 + x = 25.0499501 Solving -25 + x = 25.0499501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 25.0499501 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.0499501 + 25 x = 25.0499501 + 25 Combine like terms: 25.0499501 + 25 = 50.0499501 x = 50.0499501 Simplifying x = 50.0499501Subproblem 2
x + -25 = -25.0499501 Simplifying x + -25 = -25.0499501 Reorder the terms: -25 + x = -25.0499501 Solving -25 + x = -25.0499501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -25.0499501 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.0499501 + 25 x = -25.0499501 + 25 Combine like terms: -25.0499501 + 25 = -0.0499501 x = -0.0499501 Simplifying x = -0.0499501Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.0499501, -0.0499501}
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