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Simplifying y * y + 6y + -100 = 0 Multiply y * y y2 + 6y + -100 = 0 Reorder the terms: -100 + 6y + y2 = 0 Solving -100 + 6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 6y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + 6y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 6y + y2 = 0 + 100 6y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 6y + y2 = 100 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 100 + 9 Reorder the terms: 9 + 6y + y2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + 6y + y2 = 109 Factor a perfect square on the left side: (y + 3)(y + 3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (y + 3) equal to 10.440306509 and -10.440306509.Subproblem 1
y + 3 = 10.440306509 Simplifying y + 3 = 10.440306509 Reorder the terms: 3 + y = 10.440306509 Solving 3 + y = 10.440306509 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + y = 10.440306509 + -3 y = 10.440306509 + -3 Combine like terms: 10.440306509 + -3 = 7.440306509 y = 7.440306509 Simplifying y = 7.440306509Subproblem 2
y + 3 = -10.440306509 Simplifying y + 3 = -10.440306509 Reorder the terms: 3 + y = -10.440306509 Solving 3 + y = -10.440306509 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + y = -10.440306509 + -3 y = -10.440306509 + -3 Combine like terms: -10.440306509 + -3 = -13.440306509 y = -13.440306509 Simplifying y = -13.440306509Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.440306509, -13.440306509}
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