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Simplifying 7y2 + -10y + 1 = 0 Reorder the terms: 1 + -10y + 7y2 = 0 Solving 1 + -10y + 7y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -1.428571429y + y2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1.428571429y + -0.1428571429 + y2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1.428571429y + y2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1.428571429y + y2 = 0 + -0.1428571429 -1.428571429y + y2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1.428571429y + y2 = -0.1428571429 The y term is -1.428571429y. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429y + 0.5102040819 + y2 = -0.1428571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429y + y2 = -0.1428571429 + 0.5102040819 Combine like terms: -0.1428571429 + 0.5102040819 = 0.367346939 0.5102040819 + -1.428571429y + y2 = 0.367346939 Factor a perfect square on the left side: (y + -0.7142857145)(y + -0.7142857145) = 0.367346939 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (y + -0.7142857145) equal to 0.606091527 and -0.606091527.Subproblem 1
y + -0.7142857145 = 0.606091527 Simplifying y + -0.7142857145 = 0.606091527 Reorder the terms: -0.7142857145 + y = 0.606091527 Solving -0.7142857145 + y = 0.606091527 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + y = 0.606091527 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + y = 0.606091527 + 0.7142857145 y = 0.606091527 + 0.7142857145 Combine like terms: 0.606091527 + 0.7142857145 = 1.3203772415 y = 1.3203772415 Simplifying y = 1.3203772415Subproblem 2
y + -0.7142857145 = -0.606091527 Simplifying y + -0.7142857145 = -0.606091527 Reorder the terms: -0.7142857145 + y = -0.606091527 Solving -0.7142857145 + y = -0.606091527 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + y = -0.606091527 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + y = -0.606091527 + 0.7142857145 y = -0.606091527 + 0.7142857145 Combine like terms: -0.606091527 + 0.7142857145 = 0.1081941875 y = 0.1081941875 Simplifying y = 0.1081941875Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3203772415, 0.1081941875}
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