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Simplifying 5 = x(1 + 10x) 5 = (1 * x + 10x * x) 5 = (1x + 10x2) Solving 5 = 1x + 10x2 Solving for variable 'x'. Reorder the terms: 5 + -1x + -10x2 = 1x + -1x + 10x2 + -10x2 Combine like terms: 1x + -1x = 0 5 + -1x + -10x2 = 0 + 10x2 + -10x2 5 + -1x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 5 + -1x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.5 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.1x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.1x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.1x + x2 = 0 + 0.5 0.1x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.1x + x2 = 0.5 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.5 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.5 + 0.0025 Combine like terms: 0.5 + 0.0025 = 0.5025 0.0025 + 0.1x + x2 = 0.5025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.5025 Calculate the square root of the right side: 0.708872344 Break this problem into two subproblems by setting (x + 0.05) equal to 0.708872344 and -0.708872344.Subproblem 1
x + 0.05 = 0.708872344 Simplifying x + 0.05 = 0.708872344 Reorder the terms: 0.05 + x = 0.708872344 Solving 0.05 + x = 0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.708872344 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.708872344 + -0.05 x = 0.708872344 + -0.05 Combine like terms: 0.708872344 + -0.05 = 0.658872344 x = 0.658872344 Simplifying x = 0.658872344Subproblem 2
x + 0.05 = -0.708872344 Simplifying x + 0.05 = -0.708872344 Reorder the terms: 0.05 + x = -0.708872344 Solving 0.05 + x = -0.708872344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.708872344 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.708872344 + -0.05 x = -0.708872344 + -0.05 Combine like terms: -0.708872344 + -0.05 = -0.758872344 x = -0.758872344 Simplifying x = -0.758872344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.658872344, -0.758872344}
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