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Simplifying 0 = -0.2x2 + 10x + 5 Reorder the terms: 0 = 5 + 10x + -0.2x2 Solving 0 = 5 + 10x + -0.2x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -10x + 0.2x2 = 5 + 10x + -0.2x2 + -5 + -10x + 0.2x2 Reorder the terms: -5 + -10x + 0.2x2 = 5 + -5 + 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: 5 + -5 = 0 -5 + -10x + 0.2x2 = 0 + 10x + -10x + -0.2x2 + 0.2x2 -5 + -10x + 0.2x2 = 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: 10x + -10x = 0 -5 + -10x + 0.2x2 = 0 + -0.2x2 + 0.2x2 -5 + -10x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 -5 + -10x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -25 + -50x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -50x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -50x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -50x + x2 = 0 + 25 -50x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -50x + x2 = 25 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 = 25 + 625 Reorder the terms: 625 + -50x + x2 = 25 + 625 Combine like terms: 25 + 625 = 650 625 + -50x + x2 = 650 Factor a perfect square on the left side: (x + -25)(x + -25) = 650 Calculate the square root of the right side: 25.495097568 Break this problem into two subproblems by setting (x + -25) equal to 25.495097568 and -25.495097568.Subproblem 1
x + -25 = 25.495097568 Simplifying x + -25 = 25.495097568 Reorder the terms: -25 + x = 25.495097568 Solving -25 + x = 25.495097568 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 = 25.495097568 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.495097568 + 25 x = 25.495097568 + 25 Combine like terms: 25.495097568 + 25 = 50.495097568 x = 50.495097568 Simplifying x = 50.495097568Subproblem 2
x + -25 = -25.495097568 Simplifying x + -25 = -25.495097568 Reorder the terms: -25 + x = -25.495097568 Solving -25 + x = -25.495097568 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 = -25.495097568 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.495097568 + 25 x = -25.495097568 + 25 Combine like terms: -25.495097568 + 25 = -0.495097568 x = -0.495097568 Simplifying x = -0.495097568Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.495097568, -0.495097568}
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