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Simplifying (2y + 5)(y + -4) = 4 Reorder the terms: (5 + 2y)(y + -4) = 4 Reorder the terms: (5 + 2y)(-4 + y) = 4 Multiply (5 + 2y) * (-4 + y) (5(-4 + y) + 2y * (-4 + y)) = 4 ((-4 * 5 + y * 5) + 2y * (-4 + y)) = 4 ((-20 + 5y) + 2y * (-4 + y)) = 4 (-20 + 5y + (-4 * 2y + y * 2y)) = 4 (-20 + 5y + (-8y + 2y2)) = 4 Combine like terms: 5y + -8y = -3y (-20 + -3y + 2y2) = 4 Solving -20 + -3y + 2y2 = 4 Solving for variable 'y'. Reorder the terms: -20 + -4 + -3y + 2y2 = 4 + -4 Combine like terms: -20 + -4 = -24 -24 + -3y + 2y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -24 + -3y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + -1.5y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.5y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -1.5y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.5y + y2 = 0 + 12 -1.5y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.5y + y2 = 12 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 12 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 12 + 0.5625 Combine like terms: 12 + 0.5625 = 12.5625 0.5625 + -1.5y + y2 = 12.5625 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (y + -0.75) equal to 3.54436172 and -3.54436172.Subproblem 1
y + -0.75 = 3.54436172 Simplifying y + -0.75 = 3.54436172 Reorder the terms: -0.75 + y = 3.54436172 Solving -0.75 + y = 3.54436172 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 3.54436172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 3.54436172 + 0.75 y = 3.54436172 + 0.75 Combine like terms: 3.54436172 + 0.75 = 4.29436172 y = 4.29436172 Simplifying y = 4.29436172Subproblem 2
y + -0.75 = -3.54436172 Simplifying y + -0.75 = -3.54436172 Reorder the terms: -0.75 + y = -3.54436172 Solving -0.75 + y = -3.54436172 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -3.54436172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -3.54436172 + 0.75 y = -3.54436172 + 0.75 Combine like terms: -3.54436172 + 0.75 = -2.79436172 y = -2.79436172 Simplifying y = -2.79436172Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.29436172, -2.79436172}
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