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Simplifying y2 + 7y + -19 = 0 Reorder the terms: -19 + 7y + y2 = 0 Solving -19 + 7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 7y + 19 + y2 = 0 + 19 Reorder the terms: -19 + 19 + 7y + y2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 7y + y2 = 0 + 19 7y + y2 = 0 + 19 Combine like terms: 0 + 19 = 19 7y + y2 = 19 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = 19 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 19 + 12.25 Combine like terms: 19 + 12.25 = 31.25 12.25 + 7y + y2 = 31.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (y + 3.5) equal to 5.590169944 and -5.590169944.Subproblem 1
y + 3.5 = 5.590169944 Simplifying y + 3.5 = 5.590169944 Reorder the terms: 3.5 + y = 5.590169944 Solving 3.5 + y = 5.590169944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 5.590169944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 5.590169944 + -3.5 y = 5.590169944 + -3.5 Combine like terms: 5.590169944 + -3.5 = 2.090169944 y = 2.090169944 Simplifying y = 2.090169944Subproblem 2
y + 3.5 = -5.590169944 Simplifying y + 3.5 = -5.590169944 Reorder the terms: 3.5 + y = -5.590169944 Solving 3.5 + y = -5.590169944 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -5.590169944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -5.590169944 + -3.5 y = -5.590169944 + -3.5 Combine like terms: -5.590169944 + -3.5 = -9.090169944 y = -9.090169944 Simplifying y = -9.090169944Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.090169944, -9.090169944}
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