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Simplifying (0.20 + -1x) = (x)(0.10 + x) Remove parenthesis around (0.20 + -1x) 0.20 + -1x = (x)(0.10 + x) 0.20 + -1x = (0.10 * x + x * x) 0.20 + -1x = (0.10x + x2) Solving 0.20 + -1x = 0.10x + x2 Solving for variable 'x'. Combine like terms: -1x + -0.10x = -1.1x 0.20 + -1.1x + -1x2 = 0.10x + x2 + -0.10x + -1x2 Reorder the terms: 0.20 + -1.1x + -1x2 = 0.10x + -0.10x + x2 + -1x2 Combine like terms: 0.10x + -0.10x = 0.00 0.20 + -1.1x + -1x2 = 0.00 + x2 + -1x2 0.20 + -1.1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.20 + -1.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.2 + 1.1x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.1x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.1x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.1x + x2 = 0 + 0.2 1.1x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.1x + x2 = 0.2 The x term is 1.1x. Take half its coefficient (0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. 1.1x + 0.3025 + x2 = 0.2 + 0.3025 Reorder the terms: 0.3025 + 1.1x + x2 = 0.2 + 0.3025 Combine like terms: 0.2 + 0.3025 = 0.5025 0.3025 + 1.1x + x2 = 0.5025 Factor a perfect square on the left side: (x + 0.55)(x + 0.55) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + 0.55) equal to 0.708872344 and -0.708872344.Subproblem 1
x + 0.55 = 0.708872344 Simplifying x + 0.55 = 0.708872344 Reorder the terms: 0.55 + x = 0.708872344 Solving 0.55 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = 0.708872344 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = 0.708872344 + -0.55 x = 0.708872344 + -0.55 Combine like terms: 0.708872344 + -0.55 = 0.158872344 x = 0.158872344 Simplifying x = 0.158872344Subproblem 2
x + 0.55 = -0.708872344 Simplifying x + 0.55 = -0.708872344 Reorder the terms: 0.55 + x = -0.708872344 Solving 0.55 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + x = -0.708872344 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + x = -0.708872344 + -0.55 x = -0.708872344 + -0.55 Combine like terms: -0.708872344 + -0.55 = -1.258872344 x = -1.258872344 Simplifying x = -1.258872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158872344, -1.258872344}
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