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Simplifying 7y2 + -6y + -9 = 0 Reorder the terms: -9 + -6y + 7y2 = 0 Solving -9 + -6y + 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 + -0.8571428571y + y2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.8571428571y + 1.285714286 + y2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.8571428571y + y2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.8571428571y + y2 = 0 + 1.285714286 -0.8571428571y + y2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.8571428571y + y2 = 1.285714286 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 = 1.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571y + y2 = 1.285714286 + 0.1836734694 Combine like terms: 1.285714286 + 0.1836734694 = 1.4693877554 0.1836734694 + -0.8571428571y + y2 = 1.4693877554 Factor a perfect square on the left side: (y + -0.4285714286)(y + -0.4285714286) = 1.4693877554 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (y + -0.4285714286) equal to 1.212183054 and -1.212183054.Subproblem 1
y + -0.4285714286 = 1.212183054 Simplifying y + -0.4285714286 = 1.212183054 Reorder the terms: -0.4285714286 + y = 1.212183054 Solving -0.4285714286 + y = 1.212183054 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 = 1.212183054 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + y = 1.212183054 + 0.4285714286 y = 1.212183054 + 0.4285714286 Combine like terms: 1.212183054 + 0.4285714286 = 1.6407544826 y = 1.6407544826 Simplifying y = 1.6407544826Subproblem 2
y + -0.4285714286 = -1.212183054 Simplifying y + -0.4285714286 = -1.212183054 Reorder the terms: -0.4285714286 + y = -1.212183054 Solving -0.4285714286 + y = -1.212183054 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 = -1.212183054 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + y = -1.212183054 + 0.4285714286 y = -1.212183054 + 0.4285714286 Combine like terms: -1.212183054 + 0.4285714286 = -0.7836116254 y = -0.7836116254 Simplifying y = -0.7836116254Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6407544826, -0.7836116254}
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