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Simplifying 5y2 + y + 1y = 4 Reorder the terms: y + 1y + 5y2 = 4 Combine like terms: y + 1y = 2y 2y + 5y2 = 4 Solving 2y + 5y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 2y + 5y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 2y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.4y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.4y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.4y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.4y + y2 = 0 + 0.8 0.4y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.4y + y2 = 0.8 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 0.8 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + 0.4y + y2 = 0.84 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (y + 0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
y + 0.2 = 0.916515139 Simplifying y + 0.2 = 0.916515139 Reorder the terms: 0.2 + y = 0.916515139 Solving 0.2 + y = 0.916515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 0.916515139 + -0.2 y = 0.916515139 + -0.2 Combine like terms: 0.916515139 + -0.2 = 0.716515139 y = 0.716515139 Simplifying y = 0.716515139Subproblem 2
y + 0.2 = -0.916515139 Simplifying y + 0.2 = -0.916515139 Reorder the terms: 0.2 + y = -0.916515139 Solving 0.2 + y = -0.916515139 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -0.916515139 + -0.2 y = -0.916515139 + -0.2 Combine like terms: -0.916515139 + -0.2 = -1.116515139 y = -1.116515139 Simplifying y = -1.116515139Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.716515139, -1.116515139}
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