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Simplifying 0.2x2 + 10x + 5 = 0 Reorder the terms: 5 + 10x + 0.2x2 = 0 Solving 5 + 10x + 0.2x2 = 0 Solving for variable 'x'. 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 = 600 625 + 50x + x2 = 600 Factor a perfect square on the left side: (x + 25)(x + 25) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + 25) equal to 24.494897428 and -24.494897428.Subproblem 1
x + 25 = 24.494897428 Simplifying x + 25 = 24.494897428 Reorder the terms: 25 + x = 24.494897428 Solving 25 + x = 24.494897428 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 = 24.494897428 + -25 Combine like terms: 25 + -25 = 0 0 + x = 24.494897428 + -25 x = 24.494897428 + -25 Combine like terms: 24.494897428 + -25 = -0.505102572 x = -0.505102572 Simplifying x = -0.505102572Subproblem 2
x + 25 = -24.494897428 Simplifying x + 25 = -24.494897428 Reorder the terms: 25 + x = -24.494897428 Solving 25 + x = -24.494897428 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 = -24.494897428 + -25 Combine like terms: 25 + -25 = 0 0 + x = -24.494897428 + -25 x = -24.494897428 + -25 Combine like terms: -24.494897428 + -25 = -49.494897428 x = -49.494897428 Simplifying x = -49.494897428Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.505102572, -49.494897428}
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