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Simplifying 49x2 + -52x + 1 = 0 Reorder the terms: 1 + -52x + 49x2 = 0 Solving 1 + -52x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.02040816327 + -1.06122449x + x2 = 0 Move the constant term to the right: Add '-0.02040816327' to each side of the equation. 0.02040816327 + -1.06122449x + -0.02040816327 + x2 = 0 + -0.02040816327 Reorder the terms: 0.02040816327 + -0.02040816327 + -1.06122449x + x2 = 0 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + -1.06122449x + x2 = 0 + -0.02040816327 -1.06122449x + x2 = 0 + -0.02040816327 Combine like terms: 0 + -0.02040816327 = -0.02040816327 -1.06122449x + x2 = -0.02040816327 The x term is -1.06122449x. Take half its coefficient (-0.530612245). Square it (0.2815493545) and add it to both sides. Add '0.2815493545' to each side of the equation. -1.06122449x + 0.2815493545 + x2 = -0.02040816327 + 0.2815493545 Reorder the terms: 0.2815493545 + -1.06122449x + x2 = -0.02040816327 + 0.2815493545 Combine like terms: -0.02040816327 + 0.2815493545 = 0.26114119123 0.2815493545 + -1.06122449x + x2 = 0.26114119123 Factor a perfect square on the left side: (x + -0.530612245)(x + -0.530612245) = 0.26114119123 Calculate the square root of the right side: 0.511019756 Break this problem into two subproblems by setting (x + -0.530612245) equal to 0.511019756 and -0.511019756.Subproblem 1
x + -0.530612245 = 0.511019756 Simplifying x + -0.530612245 = 0.511019756 Reorder the terms: -0.530612245 + x = 0.511019756 Solving -0.530612245 + x = 0.511019756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + x = 0.511019756 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + x = 0.511019756 + 0.530612245 x = 0.511019756 + 0.530612245 Combine like terms: 0.511019756 + 0.530612245 = 1.041632001 x = 1.041632001 Simplifying x = 1.041632001Subproblem 2
x + -0.530612245 = -0.511019756 Simplifying x + -0.530612245 = -0.511019756 Reorder the terms: -0.530612245 + x = -0.511019756 Solving -0.530612245 + x = -0.511019756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + x = -0.511019756 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + x = -0.511019756 + 0.530612245 x = -0.511019756 + 0.530612245 Combine like terms: -0.511019756 + 0.530612245 = 0.019592489 x = 0.019592489 Simplifying x = 0.019592489Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041632001, 0.019592489}
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