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Simplifying 4y + 8 + 5y = y2 + 3 Reorder the terms: 8 + 4y + 5y = y2 + 3 Combine like terms: 4y + 5y = 9y 8 + 9y = y2 + 3 Reorder the terms: 8 + 9y = 3 + y2 Solving 8 + 9y = 3 + y2 Solving for variable 'y'. Reorder the terms: 8 + -3 + 9y + -1y2 = 3 + y2 + -3 + -1y2 Combine like terms: 8 + -3 = 5 5 + 9y + -1y2 = 3 + y2 + -3 + -1y2 Reorder the terms: 5 + 9y + -1y2 = 3 + -3 + y2 + -1y2 Combine like terms: 3 + -3 = 0 5 + 9y + -1y2 = 0 + y2 + -1y2 5 + 9y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 5 + 9y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -9y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -9y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -9y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9y + y2 = 0 + 5 -9y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -9y + y2 = 5 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 5 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 5 + 20.25 Combine like terms: 5 + 20.25 = 25.25 20.25 + -9y + y2 = 25.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (y + -4.5) equal to 5.024937811 and -5.024937811.Subproblem 1
y + -4.5 = 5.024937811 Simplifying y + -4.5 = 5.024937811 Reorder the terms: -4.5 + y = 5.024937811 Solving -4.5 + y = 5.024937811 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 5.024937811 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 5.024937811 + 4.5 y = 5.024937811 + 4.5 Combine like terms: 5.024937811 + 4.5 = 9.524937811 y = 9.524937811 Simplifying y = 9.524937811Subproblem 2
y + -4.5 = -5.024937811 Simplifying y + -4.5 = -5.024937811 Reorder the terms: -4.5 + y = -5.024937811 Solving -4.5 + y = -5.024937811 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -5.024937811 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -5.024937811 + 4.5 y = -5.024937811 + 4.5 Combine like terms: -5.024937811 + 4.5 = -0.524937811 y = -0.524937811 Simplifying y = -0.524937811Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.524937811, -0.524937811}
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