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Simplifying 49y2 + -70y + -14 = 0 Reorder the terms: -14 + -70y + 49y2 = 0 Solving -14 + -70y + 49y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7'. 7(-2 + -10y + 7y2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -10y + 7y2)' equal to zero and attempt to solve: Simplifying -2 + -10y + 7y2 = 0 Solving -2 + -10y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -1.428571429y + y2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -1.428571429y + 0.2857142857 + y2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -1.428571429y + y2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -1.428571429y + y2 = 0 + 0.2857142857 -1.428571429y + y2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -1.428571429y + y2 = 0.2857142857 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 = 0.2857142857 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429y + y2 = 0.2857142857 + 0.5102040819 Combine like terms: 0.2857142857 + 0.5102040819 = 0.7959183676 0.5102040819 + -1.428571429y + y2 = 0.7959183676 Factor a perfect square on the left side: (y + -0.7142857145)(y + -0.7142857145) = 0.7959183676 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (y + -0.7142857145) equal to 0.892142571 and -0.892142571.Subproblem 1
y + -0.7142857145 = 0.892142571 Simplifying y + -0.7142857145 = 0.892142571 Reorder the terms: -0.7142857145 + y = 0.892142571 Solving -0.7142857145 + y = 0.892142571 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 = 0.892142571 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + y = 0.892142571 + 0.7142857145 y = 0.892142571 + 0.7142857145 Combine like terms: 0.892142571 + 0.7142857145 = 1.6064282855 y = 1.6064282855 Simplifying y = 1.6064282855Subproblem 2
y + -0.7142857145 = -0.892142571 Simplifying y + -0.7142857145 = -0.892142571 Reorder the terms: -0.7142857145 + y = -0.892142571 Solving -0.7142857145 + y = -0.892142571 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 = -0.892142571 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + y = -0.892142571 + 0.7142857145 y = -0.892142571 + 0.7142857145 Combine like terms: -0.892142571 + 0.7142857145 = -0.1778568565 y = -0.1778568565 Simplifying y = -0.1778568565Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6064282855, -0.1778568565}Solution
y = {1.6064282855, -0.1778568565}
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