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Simplifying 4y2 = 7 + 15y Solving 4y2 = 7 + 15y Solving for variable 'y'. Reorder the terms: -7 + -15y + 4y2 = 7 + 15y + -7 + -15y Reorder the terms: -7 + -15y + 4y2 = 7 + -7 + 15y + -15y Combine like terms: 7 + -7 = 0 -7 + -15y + 4y2 = 0 + 15y + -15y -7 + -15y + 4y2 = 15y + -15y Combine like terms: 15y + -15y = 0 -7 + -15y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -3.75y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -3.75y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -3.75y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -3.75y + y2 = 0 + 1.75 -3.75y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -3.75y + y2 = 1.75 The y term is -3.75y. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75y + 3.515625 + y2 = 1.75 + 3.515625 Reorder the terms: 3.515625 + -3.75y + y2 = 1.75 + 3.515625 Combine like terms: 1.75 + 3.515625 = 5.265625 3.515625 + -3.75y + y2 = 5.265625 Factor a perfect square on the left side: (y + -1.875)(y + -1.875) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (y + -1.875) equal to 2.294694969 and -2.294694969.Subproblem 1
y + -1.875 = 2.294694969 Simplifying y + -1.875 = 2.294694969 Reorder the terms: -1.875 + y = 2.294694969 Solving -1.875 + y = 2.294694969 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + y = 2.294694969 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + y = 2.294694969 + 1.875 y = 2.294694969 + 1.875 Combine like terms: 2.294694969 + 1.875 = 4.169694969 y = 4.169694969 Simplifying y = 4.169694969Subproblem 2
y + -1.875 = -2.294694969 Simplifying y + -1.875 = -2.294694969 Reorder the terms: -1.875 + y = -2.294694969 Solving -1.875 + y = -2.294694969 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + y = -2.294694969 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + y = -2.294694969 + 1.875 y = -2.294694969 + 1.875 Combine like terms: -2.294694969 + 1.875 = -0.419694969 y = -0.419694969 Simplifying y = -0.419694969Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.169694969, -0.419694969}
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