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Simplifying 25y2 + 10y = 10 Reorder the terms: 10y + 25y2 = 10 Solving 10y + 25y2 = 10 Solving for variable 'y'. Reorder the terms: -10 + 10y + 25y2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 10y + 25y2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 2y + 5y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 2y + 5y2)' equal to zero and attempt to solve: Simplifying -2 + 2y + 5y2 = 0 Solving -2 + 2y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 0.4y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.4y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.4y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.4y + y2 = 0 + 0.4 0.4y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.4y + y2 = 0.4 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 = 0.4 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 0.4 + 0.04 Combine like terms: 0.4 + 0.04 = 0.44 0.04 + 0.4y + y2 = 0.44 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (y + 0.2) equal to 0.663324958 and -0.663324958.Subproblem 1
y + 0.2 = 0.663324958 Simplifying y + 0.2 = 0.663324958 Reorder the terms: 0.2 + y = 0.663324958 Solving 0.2 + y = 0.663324958 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 = 0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 0.663324958 + -0.2 y = 0.663324958 + -0.2 Combine like terms: 0.663324958 + -0.2 = 0.463324958 y = 0.463324958 Simplifying y = 0.463324958Subproblem 2
y + 0.2 = -0.663324958 Simplifying y + 0.2 = -0.663324958 Reorder the terms: 0.2 + y = -0.663324958 Solving 0.2 + y = -0.663324958 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 = -0.663324958 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -0.663324958 + -0.2 y = -0.663324958 + -0.2 Combine like terms: -0.663324958 + -0.2 = -0.863324958 y = -0.863324958 Simplifying y = -0.863324958Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.463324958, -0.863324958}Solution
y = {0.463324958, -0.863324958}
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