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Simplifying 9y2 + -6y + -4 = 0 Reorder the terms: -4 + -6y + 9y2 = 0 Solving -4 + -6y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.6666666667y + 0.4444444444 + y2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.6666666667y + y2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.6666666667y + y2 = 0 + 0.4444444444 -0.6666666667y + y2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.6666666667y + y2 = 0.4444444444 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = 0.4444444444 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = 0.4444444444 + 0.1111111112 Combine like terms: 0.4444444444 + 0.1111111112 = 0.5555555556 0.1111111112 + -0.6666666667y + y2 = 0.5555555556 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = 0.5555555556 Calculate the square root of the right side: 0.745355993 Break this problem into two subproblems by setting (y + -0.3333333334) equal to 0.745355993 and -0.745355993.Subproblem 1
y + -0.3333333334 = 0.745355993 Simplifying y + -0.3333333334 = 0.745355993 Reorder the terms: -0.3333333334 + y = 0.745355993 Solving -0.3333333334 + y = 0.745355993 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = 0.745355993 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = 0.745355993 + 0.3333333334 y = 0.745355993 + 0.3333333334 Combine like terms: 0.745355993 + 0.3333333334 = 1.0786893264 y = 1.0786893264 Simplifying y = 1.0786893264Subproblem 2
y + -0.3333333334 = -0.745355993 Simplifying y + -0.3333333334 = -0.745355993 Reorder the terms: -0.3333333334 + y = -0.745355993 Solving -0.3333333334 + y = -0.745355993 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = -0.745355993 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = -0.745355993 + 0.3333333334 y = -0.745355993 + 0.3333333334 Combine like terms: -0.745355993 + 0.3333333334 = -0.4120226596 y = -0.4120226596 Simplifying y = -0.4120226596Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.0786893264, -0.4120226596}
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