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Simplifying 0.1x2 + 2x + -5 = 0 Reorder the terms: -5 + 2x + 0.1x2 = 0 Solving -5 + 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'. -50 + 20x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 20x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 20x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 20x + x2 = 0 + 50 20x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 20x + x2 = 50 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 = 50 + 100 Reorder the terms: 100 + 20x + x2 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + 20x + x2 = 150 Factor a perfect square on the left side: (x + 10)(x + 10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + 10) equal to 12.247448714 and -12.247448714.Subproblem 1
x + 10 = 12.247448714 Simplifying x + 10 = 12.247448714 Reorder the terms: 10 + x = 12.247448714 Solving 10 + x = 12.247448714 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 = 12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.247448714 + -10 x = 12.247448714 + -10 Combine like terms: 12.247448714 + -10 = 2.247448714 x = 2.247448714 Simplifying x = 2.247448714Subproblem 2
x + 10 = -12.247448714 Simplifying x + 10 = -12.247448714 Reorder the terms: 10 + x = -12.247448714 Solving 10 + x = -12.247448714 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 = -12.247448714 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.247448714 + -10 x = -12.247448714 + -10 Combine like terms: -12.247448714 + -10 = -22.247448714 x = -22.247448714 Simplifying x = -22.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.247448714, -22.247448714}
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