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Simplifying 7y2 + -20y + 9 = 0 Reorder the terms: 9 + -20y + 7y2 = 0 Solving 9 + -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'. 1.285714286 + -2.857142857y + y2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -2.857142857y + -1.285714286 + y2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -2.857142857y + y2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -2.857142857y + y2 = 0 + -1.285714286 -2.857142857y + y2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -2.857142857y + y2 = -1.285714286 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 = -1.285714286 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857y + y2 = -1.285714286 + 2.040816328 Combine like terms: -1.285714286 + 2.040816328 = 0.755102042 2.040816328 + -2.857142857y + y2 = 0.755102042 Factor a perfect square on the left side: (y + -1.428571429)(y + -1.428571429) = 0.755102042 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (y + -1.428571429) equal to 0.868966076 and -0.868966076.Subproblem 1
y + -1.428571429 = 0.868966076 Simplifying y + -1.428571429 = 0.868966076 Reorder the terms: -1.428571429 + y = 0.868966076 Solving -1.428571429 + y = 0.868966076 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 = 0.868966076 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = 0.868966076 + 1.428571429 y = 0.868966076 + 1.428571429 Combine like terms: 0.868966076 + 1.428571429 = 2.297537505 y = 2.297537505 Simplifying y = 2.297537505Subproblem 2
y + -1.428571429 = -0.868966076 Simplifying y + -1.428571429 = -0.868966076 Reorder the terms: -1.428571429 + y = -0.868966076 Solving -1.428571429 + y = -0.868966076 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 = -0.868966076 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + y = -0.868966076 + 1.428571429 y = -0.868966076 + 1.428571429 Combine like terms: -0.868966076 + 1.428571429 = 0.559605353 y = 0.559605353 Simplifying y = 0.559605353Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.297537505, 0.559605353}
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