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Simplifying 0.1x2 + 2x + -16 = 0 Reorder the terms: -16 + 2x + 0.1x2 = 0 Solving -16 + 2x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -160 + 20x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 20x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 20x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 20x + x2 = 0 + 160 20x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 20x + x2 = 160 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 = 160 + 100 Reorder the terms: 100 + 20x + x2 = 160 + 100 Combine like terms: 160 + 100 = 260 100 + 20x + x2 = 260 Factor a perfect square on the left side: (x + 10)(x + 10) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + 10) equal to 16.124515497 and -16.124515497.Subproblem 1
x + 10 = 16.124515497 Simplifying x + 10 = 16.124515497 Reorder the terms: 10 + x = 16.124515497 Solving 10 + x = 16.124515497 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 = 16.124515497 + -10 Combine like terms: 10 + -10 = 0 0 + x = 16.124515497 + -10 x = 16.124515497 + -10 Combine like terms: 16.124515497 + -10 = 6.124515497 x = 6.124515497 Simplifying x = 6.124515497Subproblem 2
x + 10 = -16.124515497 Simplifying x + 10 = -16.124515497 Reorder the terms: 10 + x = -16.124515497 Solving 10 + x = -16.124515497 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 = -16.124515497 + -10 Combine like terms: 10 + -10 = 0 0 + x = -16.124515497 + -10 x = -16.124515497 + -10 Combine like terms: -16.124515497 + -10 = -26.124515497 x = -26.124515497 Simplifying x = -26.124515497Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.124515497, -26.124515497}
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