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Simplifying 50y2 + 25y + -84 = 0 Reorder the terms: -84 + 25y + 50y2 = 0 Solving -84 + 25y + 50y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.68 + 0.5y + y2 = 0 Move the constant term to the right: Add '1.68' to each side of the equation. -1.68 + 0.5y + 1.68 + y2 = 0 + 1.68 Reorder the terms: -1.68 + 1.68 + 0.5y + y2 = 0 + 1.68 Combine like terms: -1.68 + 1.68 = 0.00 0.00 + 0.5y + y2 = 0 + 1.68 0.5y + y2 = 0 + 1.68 Combine like terms: 0 + 1.68 = 1.68 0.5y + y2 = 1.68 The y term is 0.5y. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y + 0.0625 + y2 = 1.68 + 0.0625 Reorder the terms: 0.0625 + 0.5y + y2 = 1.68 + 0.0625 Combine like terms: 1.68 + 0.0625 = 1.7425 0.0625 + 0.5y + y2 = 1.7425 Factor a perfect square on the left side: (y + 0.25)(y + 0.25) = 1.7425 Calculate the square root of the right side: 1.320037878 Break this problem into two subproblems by setting (y + 0.25) equal to 1.320037878 and -1.320037878.Subproblem 1
y + 0.25 = 1.320037878 Simplifying y + 0.25 = 1.320037878 Reorder the terms: 0.25 + y = 1.320037878 Solving 0.25 + y = 1.320037878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = 1.320037878 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = 1.320037878 + -0.25 y = 1.320037878 + -0.25 Combine like terms: 1.320037878 + -0.25 = 1.070037878 y = 1.070037878 Simplifying y = 1.070037878Subproblem 2
y + 0.25 = -1.320037878 Simplifying y + 0.25 = -1.320037878 Reorder the terms: 0.25 + y = -1.320037878 Solving 0.25 + y = -1.320037878 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + y = -1.320037878 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + y = -1.320037878 + -0.25 y = -1.320037878 + -0.25 Combine like terms: -1.320037878 + -0.25 = -1.570037878 y = -1.570037878 Simplifying y = -1.570037878Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.070037878, -1.570037878}
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