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Simplifying y2 + -6y = 5 + -6y2 Reorder the terms: -6y + y2 = 5 + -6y2 Solving -6y + y2 = 5 + -6y2 Solving for variable 'y'. Reorder the terms: -5 + -6y + y2 + 6y2 = 5 + -6y2 + -5 + 6y2 Combine like terms: y2 + 6y2 = 7y2 -5 + -6y + 7y2 = 5 + -6y2 + -5 + 6y2 Reorder the terms: -5 + -6y + 7y2 = 5 + -5 + -6y2 + 6y2 Combine like terms: 5 + -5 = 0 -5 + -6y + 7y2 = 0 + -6y2 + 6y2 -5 + -6y + 7y2 = -6y2 + 6y2 Combine like terms: -6y2 + 6y2 = 0 -5 + -6y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.8571428571y + y2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.8571428571y + 0.7142857143 + y2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.8571428571y + y2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.8571428571y + y2 = 0 + 0.7142857143 -0.8571428571y + y2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.8571428571y + y2 = 0.7142857143 The y term is -0.8571428571y. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571y + 0.1836734694 + y2 = 0.7142857143 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571y + y2 = 0.7142857143 + 0.1836734694 Combine like terms: 0.7142857143 + 0.1836734694 = 0.8979591837 0.1836734694 + -0.8571428571y + y2 = 0.8979591837 Factor a perfect square on the left side: (y + -0.4285714286)(y + -0.4285714286) = 0.8979591837 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (y + -0.4285714286) equal to 0.947607083 and -0.947607083.Subproblem 1
y + -0.4285714286 = 0.947607083 Simplifying y + -0.4285714286 = 0.947607083 Reorder the terms: -0.4285714286 + y = 0.947607083 Solving -0.4285714286 + y = 0.947607083 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + y = 0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + y = 0.947607083 + 0.4285714286 y = 0.947607083 + 0.4285714286 Combine like terms: 0.947607083 + 0.4285714286 = 1.3761785116 y = 1.3761785116 Simplifying y = 1.3761785116Subproblem 2
y + -0.4285714286 = -0.947607083 Simplifying y + -0.4285714286 = -0.947607083 Reorder the terms: -0.4285714286 + y = -0.947607083 Solving -0.4285714286 + y = -0.947607083 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + y = -0.947607083 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + y = -0.947607083 + 0.4285714286 y = -0.947607083 + 0.4285714286 Combine like terms: -0.947607083 + 0.4285714286 = -0.5190356544 y = -0.5190356544 Simplifying y = -0.5190356544Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3761785116, -0.5190356544}
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