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Simplifying 0.1x2 + 2x = 50 Reorder the terms: 2x + 0.1x2 = 50 Solving 2x + 0.1x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 2x + 0.1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 2x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -500 + 20x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 20x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 20x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 20x + x2 = 0 + 500 20x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 20x + x2 = 500 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 500 + 100 Reorder the terms: 100 + 20x + x2 = 500 + 100 Combine like terms: 500 + 100 = 600 100 + 20x + x2 = 600 Factor a perfect square on the left side: (x + 10)(x + 10) = 600 Calculate the square root of the right side: 24.494897428 Break this problem into two subproblems by setting (x + 10) equal to 24.494897428 and -24.494897428.Subproblem 1
x + 10 = 24.494897428 Simplifying x + 10 = 24.494897428 Reorder the terms: 10 + x = 24.494897428 Solving 10 + x = 24.494897428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + x = 24.494897428 + -10 x = 24.494897428 + -10 Combine like terms: 24.494897428 + -10 = 14.494897428 x = 14.494897428 Simplifying x = 14.494897428Subproblem 2
x + 10 = -24.494897428 Simplifying x + 10 = -24.494897428 Reorder the terms: 10 + x = -24.494897428 Solving 10 + x = -24.494897428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + x = -24.494897428 + -10 x = -24.494897428 + -10 Combine like terms: -24.494897428 + -10 = -34.494897428 x = -34.494897428 Simplifying x = -34.494897428Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.494897428, -34.494897428}
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