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Simplifying 8(y2 + -9) + 2y = 5y + -1 Reorder the terms: 8(-9 + y2) + 2y = 5y + -1 (-9 * 8 + y2 * 8) + 2y = 5y + -1 (-72 + 8y2) + 2y = 5y + -1 Reorder the terms: -72 + 2y + 8y2 = 5y + -1 Reorder the terms: -72 + 2y + 8y2 = -1 + 5y Solving -72 + 2y + 8y2 = -1 + 5y Solving for variable 'y'. Reorder the terms: -72 + 1 + 2y + -5y + 8y2 = -1 + 5y + 1 + -5y Combine like terms: -72 + 1 = -71 -71 + 2y + -5y + 8y2 = -1 + 5y + 1 + -5y Combine like terms: 2y + -5y = -3y -71 + -3y + 8y2 = -1 + 5y + 1 + -5y Reorder the terms: -71 + -3y + 8y2 = -1 + 1 + 5y + -5y Combine like terms: -1 + 1 = 0 -71 + -3y + 8y2 = 0 + 5y + -5y -71 + -3y + 8y2 = 5y + -5y Combine like terms: 5y + -5y = 0 -71 + -3y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.875 + -0.375y + y2 = 0 Move the constant term to the right: Add '8.875' to each side of the equation. -8.875 + -0.375y + 8.875 + y2 = 0 + 8.875 Reorder the terms: -8.875 + 8.875 + -0.375y + y2 = 0 + 8.875 Combine like terms: -8.875 + 8.875 = 0.000 0.000 + -0.375y + y2 = 0 + 8.875 -0.375y + y2 = 0 + 8.875 Combine like terms: 0 + 8.875 = 8.875 -0.375y + y2 = 8.875 The y term is -0.375y. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375y + 0.03515625 + y2 = 8.875 + 0.03515625 Reorder the terms: 0.03515625 + -0.375y + y2 = 8.875 + 0.03515625 Combine like terms: 8.875 + 0.03515625 = 8.91015625 0.03515625 + -0.375y + y2 = 8.91015625 Factor a perfect square on the left side: (y + -0.1875)(y + -0.1875) = 8.91015625 Calculate the square root of the right side: 2.984988484 Break this problem into two subproblems by setting (y + -0.1875) equal to 2.984988484 and -2.984988484.Subproblem 1
y + -0.1875 = 2.984988484 Simplifying y + -0.1875 = 2.984988484 Reorder the terms: -0.1875 + y = 2.984988484 Solving -0.1875 + y = 2.984988484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + y = 2.984988484 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + y = 2.984988484 + 0.1875 y = 2.984988484 + 0.1875 Combine like terms: 2.984988484 + 0.1875 = 3.172488484 y = 3.172488484 Simplifying y = 3.172488484Subproblem 2
y + -0.1875 = -2.984988484 Simplifying y + -0.1875 = -2.984988484 Reorder the terms: -0.1875 + y = -2.984988484 Solving -0.1875 + y = -2.984988484 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + y = -2.984988484 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + y = -2.984988484 + 0.1875 y = -2.984988484 + 0.1875 Combine like terms: -2.984988484 + 0.1875 = -2.797488484 y = -2.797488484 Simplifying y = -2.797488484Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.172488484, -2.797488484}
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