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Simplifying 7y2 + -20y + 5 = 0 Reorder the terms: 5 + -20y + 7y2 = 0 Solving 5 + -20y + 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'. 0.7142857143 + -2.857142857y + y2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -2.857142857y + -0.7142857143 + y2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -2.857142857y + y2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -2.857142857y + y2 = 0 + -0.7142857143 -2.857142857y + y2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -2.857142857y + y2 = -0.7142857143 The y term is -2.857142857y. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857y + 2.040816328 + y2 = -0.7142857143 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857y + y2 = -0.7142857143 + 2.040816328 Combine like terms: -0.7142857143 + 2.040816328 = 1.3265306137 2.040816328 + -2.857142857y + y2 = 1.3265306137 Factor a perfect square on the left side: (y + -1.428571429)(y + -1.428571429) = 1.3265306137 Calculate the square root of the right side: 1.151751108 Break this problem into two subproblems by setting (y + -1.428571429) equal to 1.151751108 and -1.151751108.Subproblem 1
y + -1.428571429 = 1.151751108 Simplifying y + -1.428571429 = 1.151751108 Reorder the terms: -1.428571429 + y = 1.151751108 Solving -1.428571429 + y = 1.151751108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + y = 1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = 1.151751108 + 1.428571429 y = 1.151751108 + 1.428571429 Combine like terms: 1.151751108 + 1.428571429 = 2.580322537 y = 2.580322537 Simplifying y = 2.580322537Subproblem 2
y + -1.428571429 = -1.151751108 Simplifying y + -1.428571429 = -1.151751108 Reorder the terms: -1.428571429 + y = -1.151751108 Solving -1.428571429 + y = -1.151751108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + y = -1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = -1.151751108 + 1.428571429 y = -1.151751108 + 1.428571429 Combine like terms: -1.151751108 + 1.428571429 = 0.276820321 y = 0.276820321 Simplifying y = 0.276820321Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.580322537, 0.276820321}
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