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Simplifying 0.2y2 + -2 = -0.3y Reorder the terms: -2 + 0.2y2 = -0.3y Solving -2 + 0.2y2 = -0.3y Solving for variable 'y'. Reorder the terms: -2 + 0.3y + 0.2y2 = -0.3y + 0.3y Combine like terms: -0.3y + 0.3y = 0.0 -2 + 0.3y + 0.2y2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -10 + 1.5y + y2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 1.5y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + 1.5y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 1.5y + y2 = 0 + 10 1.5y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 1.5y + y2 = 10 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 = 10 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = 10 + 0.5625 Combine like terms: 10 + 0.5625 = 10.5625 0.5625 + 1.5y + y2 = 10.5625 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (y + 0.75) equal to 3.25 and -3.25.Subproblem 1
y + 0.75 = 3.25 Simplifying y + 0.75 = 3.25 Reorder the terms: 0.75 + y = 3.25 Solving 0.75 + y = 3.25 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 = 3.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 3.25 + -0.75 y = 3.25 + -0.75 Combine like terms: 3.25 + -0.75 = 2.5 y = 2.5 Simplifying y = 2.5Subproblem 2
y + 0.75 = -3.25 Simplifying y + 0.75 = -3.25 Reorder the terms: 0.75 + y = -3.25 Solving 0.75 + y = -3.25 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 = -3.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -3.25 + -0.75 y = -3.25 + -0.75 Combine like terms: -3.25 + -0.75 = -4 y = -4 Simplifying y = -4Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.5, -4}
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