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Simplifying (10x * 10x) + x = 2 Reorder the terms for easier multiplication: (10 * 10x * x) + x = 2 Multiply 10 * 10 (100x * x) + x = 2 Multiply x * x (100x2) + x = 2 Reorder the terms: x + (100x2) = 2 Solving x + (100x2) = 2 Solving for variable 'x'. Reorder the terms: -2 + x + (100x2) = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + x + (100x2) = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.02 + 0.01x + x2 = 0.00 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + 0.01x + 0.02 + x2 = 0.00 + 0.02 Reorder the terms: -0.02 + 0.02 + 0.01x + x2 = 0.00 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + 0.01x + x2 = 0.00 + 0.02 0.01x + x2 = 0.00 + 0.02 Combine like terms: 0.00 + 0.02 = 0.02 0.01x + x2 = 0.02 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01x + 0.25 + x2 = 0.02 + 0.25 Reorder the terms: 0.25 + 0.01x + x2 = 0.02 + 0.25 Combine like terms: 0.02 + 0.25 = 0.27 0.25 + 0.01x + x2 = 0.27 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 0.27 Calculate the square root of the right side: 0.519615242 Break this problem into two subproblems by setting ((x) + 0.5) equal to 0.519615242 and -0.519615242.Subproblem 1
(x) + 0.5 = 0.519615242 Simplifying (x) + 0.5 = 0.519615242 x + 0.5 = 0.519615242 Reorder the terms: 0.5 + x = 0.519615242 Solving 0.5 + x = 0.519615242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.519615242 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.519615242 + -0.5 x = 0.519615242 + -0.5 Combine like terms: 0.519615242 + -0.5 = 0.019615242 x = 0.019615242 Simplifying x = 0.019615242Subproblem 2
(x) + 0.5 = -0.519615242 Simplifying (x) + 0.5 = -0.519615242 x + 0.5 = -0.519615242 Reorder the terms: 0.5 + x = -0.519615242 Solving 0.5 + x = -0.519615242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.519615242 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.519615242 + -0.5 x = -0.519615242 + -0.5 Combine like terms: -0.519615242 + -0.5 = -1.019615242 x = -1.019615242 Simplifying x = -1.019615242Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019615242, -1.019615242}
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