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Simplifying (10x * 10x) + -1x = 2 Reorder the terms for easier multiplication: (10 * 10x * x) + -1x = 2 Multiply 10 * 10 (100x * x) + -1x = 2 Multiply x * x (100x2) + -1x = 2 Reorder the terms: -1x + (100x2) = 2 Solving -1x + (100x2) = 2 Solving for variable 'x'. Reorder the terms: -2 + -1x + (100x2) = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -1x + (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 -0.01x. Take half its coefficient (-0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. -0.01x + 0.000025 + x2 = 0.02 + 0.000025 Reorder the terms: 0.000025 + -0.01x + x2 = 0.02 + 0.000025 Combine like terms: 0.02 + 0.000025 = 0.020025 0.000025 + -0.01x + x2 = 0.020025 Factor a perfect square on the left side: ((x) + -0.005)((x) + -0.005) = 0.020025 Calculate the square root of the right side: 0.141509717 Break this problem into two subproblems by setting ((x) + -0.005) equal to 0.141509717 and -0.141509717.Subproblem 1
(x) + -0.005 = 0.141509717 Simplifying (x) + -0.005 = 0.141509717 x + -0.005 = 0.141509717 Reorder the terms: -0.005 + x = 0.141509717 Solving -0.005 + x = 0.141509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = 0.141509717 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = 0.141509717 + 0.005 x = 0.141509717 + 0.005 Combine like terms: 0.141509717 + 0.005 = 0.146509717 x = 0.146509717 Simplifying x = 0.146509717Subproblem 2
(x) + -0.005 = -0.141509717 Simplifying (x) + -0.005 = -0.141509717 x + -0.005 = -0.141509717 Reorder the terms: -0.005 + x = -0.141509717 Solving -0.005 + x = -0.141509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.005' to each side of the equation. -0.005 + 0.005 + x = -0.141509717 + 0.005 Combine like terms: -0.005 + 0.005 = 0.000 0.000 + x = -0.141509717 + 0.005 x = -0.141509717 + 0.005 Combine like terms: -0.141509717 + 0.005 = -0.136509717 x = -0.136509717 Simplifying x = -0.136509717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.146509717, -0.136509717}
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