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Simplifying 7y(18y + -33) = 167 Reorder the terms: 7y(-33 + 18y) = 167 (-33 * 7y + 18y * 7y) = 167 (-231y + 126y2) = 167 Solving -231y + 126y2 = 167 Solving for variable 'y'. Reorder the terms: -167 + -231y + 126y2 = 167 + -167 Combine like terms: 167 + -167 = 0 -167 + -231y + 126y2 = 0 Begin completing the square. Divide all terms by 126 the coefficient of the squared term: Divide each side by '126'. -1.325396825 + -1.833333333y + y2 = 0 Move the constant term to the right: Add '1.325396825' to each side of the equation. -1.325396825 + -1.833333333y + 1.325396825 + y2 = 0 + 1.325396825 Reorder the terms: -1.325396825 + 1.325396825 + -1.833333333y + y2 = 0 + 1.325396825 Combine like terms: -1.325396825 + 1.325396825 = 0.000000000 0.000000000 + -1.833333333y + y2 = 0 + 1.325396825 -1.833333333y + y2 = 0 + 1.325396825 Combine like terms: 0 + 1.325396825 = 1.325396825 -1.833333333y + y2 = 1.325396825 The y term is -1.833333333y. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333y + 0.8402777775 + y2 = 1.325396825 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333y + y2 = 1.325396825 + 0.8402777775 Combine like terms: 1.325396825 + 0.8402777775 = 2.1656746025 0.8402777775 + -1.833333333y + y2 = 2.1656746025 Factor a perfect square on the left side: (y + -0.9166666665)(y + -0.9166666665) = 2.1656746025 Calculate the square root of the right side: 1.471623118 Break this problem into two subproblems by setting (y + -0.9166666665) equal to 1.471623118 and -1.471623118.Subproblem 1
y + -0.9166666665 = 1.471623118 Simplifying y + -0.9166666665 = 1.471623118 Reorder the terms: -0.9166666665 + y = 1.471623118 Solving -0.9166666665 + y = 1.471623118 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + y = 1.471623118 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + y = 1.471623118 + 0.9166666665 y = 1.471623118 + 0.9166666665 Combine like terms: 1.471623118 + 0.9166666665 = 2.3882897845 y = 2.3882897845 Simplifying y = 2.3882897845Subproblem 2
y + -0.9166666665 = -1.471623118 Simplifying y + -0.9166666665 = -1.471623118 Reorder the terms: -0.9166666665 + y = -1.471623118 Solving -0.9166666665 + y = -1.471623118 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + y = -1.471623118 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + y = -1.471623118 + 0.9166666665 y = -1.471623118 + 0.9166666665 Combine like terms: -1.471623118 + 0.9166666665 = -0.5549564515 y = -0.5549564515 Simplifying y = -0.5549564515Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.3882897845, -0.5549564515}
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