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Simplifying 5y2 + 3y + -10 = 0 Reorder the terms: -10 + 3y + 5y2 = 0 Solving -10 + 3y + 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'. -2 + 0.6y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6y + y2 = 0 + 2 0.6y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6y + y2 = 2 The y term is 0.6y. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6y + 0.09 + y2 = 2 + 0.09 Reorder the terms: 0.09 + 0.6y + y2 = 2 + 0.09 Combine like terms: 2 + 0.09 = 2.09 0.09 + 0.6y + y2 = 2.09 Factor a perfect square on the left side: (y + 0.3)(y + 0.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (y + 0.3) equal to 1.445683229 and -1.445683229.Subproblem 1
y + 0.3 = 1.445683229 Simplifying y + 0.3 = 1.445683229 Reorder the terms: 0.3 + y = 1.445683229 Solving 0.3 + y = 1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = 1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = 1.445683229 + -0.3 y = 1.445683229 + -0.3 Combine like terms: 1.445683229 + -0.3 = 1.145683229 y = 1.145683229 Simplifying y = 1.145683229Subproblem 2
y + 0.3 = -1.445683229 Simplifying y + 0.3 = -1.445683229 Reorder the terms: 0.3 + y = -1.445683229 Solving 0.3 + y = -1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = -1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = -1.445683229 + -0.3 y = -1.445683229 + -0.3 Combine like terms: -1.445683229 + -0.3 = -1.745683229 y = -1.745683229 Simplifying y = -1.745683229Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.145683229, -1.745683229}
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