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Simplifying 5 + 2(y + 4) = 5y(y + -3) + 10 Reorder the terms: 5 + 2(4 + y) = 5y(y + -3) + 10 5 + (4 * 2 + y * 2) = 5y(y + -3) + 10 5 + (8 + 2y) = 5y(y + -3) + 10 Combine like terms: 5 + 8 = 13 13 + 2y = 5y(y + -3) + 10 Reorder the terms: 13 + 2y = 5y(-3 + y) + 10 13 + 2y = (-3 * 5y + y * 5y) + 10 13 + 2y = (-15y + 5y2) + 10 Reorder the terms: 13 + 2y = 10 + -15y + 5y2 Solving 13 + 2y = 10 + -15y + 5y2 Solving for variable 'y'. Reorder the terms: 13 + -10 + 2y + 15y + -5y2 = 10 + -15y + 5y2 + -10 + 15y + -5y2 Combine like terms: 13 + -10 = 3 3 + 2y + 15y + -5y2 = 10 + -15y + 5y2 + -10 + 15y + -5y2 Combine like terms: 2y + 15y = 17y 3 + 17y + -5y2 = 10 + -15y + 5y2 + -10 + 15y + -5y2 Reorder the terms: 3 + 17y + -5y2 = 10 + -10 + -15y + 15y + 5y2 + -5y2 Combine like terms: 10 + -10 = 0 3 + 17y + -5y2 = 0 + -15y + 15y + 5y2 + -5y2 3 + 17y + -5y2 = -15y + 15y + 5y2 + -5y2 Combine like terms: -15y + 15y = 0 3 + 17y + -5y2 = 0 + 5y2 + -5y2 3 + 17y + -5y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 3 + 17y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -3.4y + y2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.4y + 0.6 + y2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.4y + y2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.4y + y2 = 0 + 0.6 -3.4y + y2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.4y + y2 = 0.6 The y term is -3.4y. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4y + 2.89 + y2 = 0.6 + 2.89 Reorder the terms: 2.89 + -3.4y + y2 = 0.6 + 2.89 Combine like terms: 0.6 + 2.89 = 3.49 2.89 + -3.4y + y2 = 3.49 Factor a perfect square on the left side: (y + -1.7)(y + -1.7) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (y + -1.7) equal to 1.868154169 and -1.868154169.Subproblem 1
y + -1.7 = 1.868154169 Simplifying y + -1.7 = 1.868154169 Reorder the terms: -1.7 + y = 1.868154169 Solving -1.7 + y = 1.868154169 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + y = 1.868154169 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = 1.868154169 + 1.7 y = 1.868154169 + 1.7 Combine like terms: 1.868154169 + 1.7 = 3.568154169 y = 3.568154169 Simplifying y = 3.568154169Subproblem 2
y + -1.7 = -1.868154169 Simplifying y + -1.7 = -1.868154169 Reorder the terms: -1.7 + y = -1.868154169 Solving -1.7 + y = -1.868154169 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + y = -1.868154169 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = -1.868154169 + 1.7 y = -1.868154169 + 1.7 Combine like terms: -1.868154169 + 1.7 = -0.168154169 y = -0.168154169 Simplifying y = -0.168154169Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.568154169, -0.168154169}
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