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Simplifying 4y2 + 15y + 2 = 0 Reorder the terms: 2 + 15y + 4y2 = 0 Solving 2 + 15y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 3.75y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 3.75y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 3.75y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 3.75y + y2 = 0 + -0.5 3.75y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 3.75y + y2 = -0.5 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 = -0.5 + 3.515625 Reorder the terms: 3.515625 + 3.75y + y2 = -0.5 + 3.515625 Combine like terms: -0.5 + 3.515625 = 3.015625 3.515625 + 3.75y + y2 = 3.015625 Factor a perfect square on the left side: (y + 1.875)(y + 1.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (y + 1.875) equal to 1.736555499 and -1.736555499.Subproblem 1
y + 1.875 = 1.736555499 Simplifying y + 1.875 = 1.736555499 Reorder the terms: 1.875 + y = 1.736555499 Solving 1.875 + y = 1.736555499 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 = 1.736555499 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + y = 1.736555499 + -1.875 y = 1.736555499 + -1.875 Combine like terms: 1.736555499 + -1.875 = -0.138444501 y = -0.138444501 Simplifying y = -0.138444501Subproblem 2
y + 1.875 = -1.736555499 Simplifying y + 1.875 = -1.736555499 Reorder the terms: 1.875 + y = -1.736555499 Solving 1.875 + y = -1.736555499 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 = -1.736555499 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + y = -1.736555499 + -1.875 y = -1.736555499 + -1.875 Combine like terms: -1.736555499 + -1.875 = -3.611555499 y = -3.611555499 Simplifying y = -3.611555499Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.138444501, -3.611555499}
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