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Simplifying 5y2 + 6y + -5 = 0 Reorder the terms: -5 + 6y + 5y2 = 0 Solving -5 + 6y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 1.2y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.2y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 1.2y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.2y + y2 = 0 + 1 1.2y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.2y + y2 = 1 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = 1 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = 1 + 0.36 Combine like terms: 1 + 0.36 = 1.36 0.36 + 1.2y + y2 = 1.36 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (y + 0.6) equal to 1.166190379 and -1.166190379.Subproblem 1
y + 0.6 = 1.166190379 Simplifying y + 0.6 = 1.166190379 Reorder the terms: 0.6 + y = 1.166190379 Solving 0.6 + y = 1.166190379 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = 1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = 1.166190379 + -0.6 y = 1.166190379 + -0.6 Combine like terms: 1.166190379 + -0.6 = 0.566190379 y = 0.566190379 Simplifying y = 0.566190379Subproblem 2
y + 0.6 = -1.166190379 Simplifying y + 0.6 = -1.166190379 Reorder the terms: 0.6 + y = -1.166190379 Solving 0.6 + y = -1.166190379 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = -1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = -1.166190379 + -0.6 y = -1.166190379 + -0.6 Combine like terms: -1.166190379 + -0.6 = -1.766190379 y = -1.766190379 Simplifying y = -1.766190379Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.566190379, -1.766190379}
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