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Simplifying 17y2 + 24y + 4 = 0 Reorder the terms: 4 + 24y + 17y2 = 0 Solving 4 + 24y + 17y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.2352941176 + 1.411764706y + y2 = 0 Move the constant term to the right: Add '-0.2352941176' to each side of the equation. 0.2352941176 + 1.411764706y + -0.2352941176 + y2 = 0 + -0.2352941176 Reorder the terms: 0.2352941176 + -0.2352941176 + 1.411764706y + y2 = 0 + -0.2352941176 Combine like terms: 0.2352941176 + -0.2352941176 = 0.0000000000 0.0000000000 + 1.411764706y + y2 = 0 + -0.2352941176 1.411764706y + y2 = 0 + -0.2352941176 Combine like terms: 0 + -0.2352941176 = -0.2352941176 1.411764706y + y2 = -0.2352941176 The y term is 1.411764706y. Take half its coefficient (0.705882353). Square it (0.4982698963) and add it to both sides. Add '0.4982698963' to each side of the equation. 1.411764706y + 0.4982698963 + y2 = -0.2352941176 + 0.4982698963 Reorder the terms: 0.4982698963 + 1.411764706y + y2 = -0.2352941176 + 0.4982698963 Combine like terms: -0.2352941176 + 0.4982698963 = 0.2629757787 0.4982698963 + 1.411764706y + y2 = 0.2629757787 Factor a perfect square on the left side: (y + 0.705882353)(y + 0.705882353) = 0.2629757787 Calculate the square root of the right side: 0.512811641 Break this problem into two subproblems by setting (y + 0.705882353) equal to 0.512811641 and -0.512811641.Subproblem 1
y + 0.705882353 = 0.512811641 Simplifying y + 0.705882353 = 0.512811641 Reorder the terms: 0.705882353 + y = 0.512811641 Solving 0.705882353 + y = 0.512811641 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.705882353' to each side of the equation. 0.705882353 + -0.705882353 + y = 0.512811641 + -0.705882353 Combine like terms: 0.705882353 + -0.705882353 = 0.000000000 0.000000000 + y = 0.512811641 + -0.705882353 y = 0.512811641 + -0.705882353 Combine like terms: 0.512811641 + -0.705882353 = -0.193070712 y = -0.193070712 Simplifying y = -0.193070712Subproblem 2
y + 0.705882353 = -0.512811641 Simplifying y + 0.705882353 = -0.512811641 Reorder the terms: 0.705882353 + y = -0.512811641 Solving 0.705882353 + y = -0.512811641 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.705882353' to each side of the equation. 0.705882353 + -0.705882353 + y = -0.512811641 + -0.705882353 Combine like terms: 0.705882353 + -0.705882353 = 0.000000000 0.000000000 + y = -0.512811641 + -0.705882353 y = -0.512811641 + -0.705882353 Combine like terms: -0.512811641 + -0.705882353 = -1.218693994 y = -1.218693994 Simplifying y = -1.218693994Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.193070712, -1.218693994}
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