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Simplifying 15y2 + -8y + -9 = 0 Reorder the terms: -9 + -8y + 15y2 = 0 Solving -9 + -8y + 15y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6 + -0.5333333333y + y2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.5333333333y + 0.6 + y2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.5333333333y + y2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.5333333333y + y2 = 0 + 0.6 -0.5333333333y + y2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.5333333333y + y2 = 0.6 The y term is -0.5333333333y. Take half its coefficient (-0.2666666667). Square it (0.07111111113) and add it to both sides. Add '0.07111111113' to each side of the equation. -0.5333333333y + 0.07111111113 + y2 = 0.6 + 0.07111111113 Reorder the terms: 0.07111111113 + -0.5333333333y + y2 = 0.6 + 0.07111111113 Combine like terms: 0.6 + 0.07111111113 = 0.67111111113 0.07111111113 + -0.5333333333y + y2 = 0.67111111113 Factor a perfect square on the left side: (y + -0.2666666667)(y + -0.2666666667) = 0.67111111113 Calculate the square root of the right side: 0.819213715 Break this problem into two subproblems by setting (y + -0.2666666667) equal to 0.819213715 and -0.819213715.Subproblem 1
y + -0.2666666667 = 0.819213715 Simplifying y + -0.2666666667 = 0.819213715 Reorder the terms: -0.2666666667 + y = 0.819213715 Solving -0.2666666667 + y = 0.819213715 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + y = 0.819213715 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + y = 0.819213715 + 0.2666666667 y = 0.819213715 + 0.2666666667 Combine like terms: 0.819213715 + 0.2666666667 = 1.0858803817 y = 1.0858803817 Simplifying y = 1.0858803817Subproblem 2
y + -0.2666666667 = -0.819213715 Simplifying y + -0.2666666667 = -0.819213715 Reorder the terms: -0.2666666667 + y = -0.819213715 Solving -0.2666666667 + y = -0.819213715 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2666666667' to each side of the equation. -0.2666666667 + 0.2666666667 + y = -0.819213715 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + y = -0.819213715 + 0.2666666667 y = -0.819213715 + 0.2666666667 Combine like terms: -0.819213715 + 0.2666666667 = -0.5525470483 y = -0.5525470483 Simplifying y = -0.5525470483Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.0858803817, -0.5525470483}
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