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Simplifying y2 + -7 = 2y2 + -18y Reorder the terms: -7 + y2 = 2y2 + -18y Reorder the terms: -7 + y2 = -18y + 2y2 Solving -7 + y2 = -18y + 2y2 Solving for variable 'y'. Reorder the terms: -7 + 18y + y2 + -2y2 = -18y + 2y2 + 18y + -2y2 Combine like terms: y2 + -2y2 = -1y2 -7 + 18y + -1y2 = -18y + 2y2 + 18y + -2y2 Reorder the terms: -7 + 18y + -1y2 = -18y + 18y + 2y2 + -2y2 Combine like terms: -18y + 18y = 0 -7 + 18y + -1y2 = 0 + 2y2 + -2y2 -7 + 18y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -7 + 18y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 7 + -18y + y2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -18y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -18y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -18y + y2 = 0 + -7 -18y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -18y + y2 = -7 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = -7 + 81 Reorder the terms: 81 + -18y + y2 = -7 + 81 Combine like terms: -7 + 81 = 74 81 + -18y + y2 = 74 Factor a perfect square on the left side: (y + -9)(y + -9) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (y + -9) equal to 8.602325267 and -8.602325267.Subproblem 1
y + -9 = 8.602325267 Simplifying y + -9 = 8.602325267 Reorder the terms: -9 + y = 8.602325267 Solving -9 + y = 8.602325267 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + y = 8.602325267 + 9 y = 8.602325267 + 9 Combine like terms: 8.602325267 + 9 = 17.602325267 y = 17.602325267 Simplifying y = 17.602325267Subproblem 2
y + -9 = -8.602325267 Simplifying y + -9 = -8.602325267 Reorder the terms: -9 + y = -8.602325267 Solving -9 + y = -8.602325267 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -8.602325267 + 9 Combine like terms: -9 + 9 = 0 0 + y = -8.602325267 + 9 y = -8.602325267 + 9 Combine like terms: -8.602325267 + 9 = 0.397674733 y = 0.397674733 Simplifying y = 0.397674733Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.602325267, 0.397674733}
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