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Simplifying y2 + 10y + -26 = 0 Reorder the terms: -26 + 10y + y2 = 0 Solving -26 + 10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 10y + 26 + y2 = 0 + 26 Reorder the terms: -26 + 26 + 10y + y2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 10y + y2 = 0 + 26 10y + y2 = 0 + 26 Combine like terms: 0 + 26 = 26 10y + y2 = 26 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 26 + 25 Reorder the terms: 25 + 10y + y2 = 26 + 25 Combine like terms: 26 + 25 = 51 25 + 10y + y2 = 51 Factor a perfect square on the left side: (y + 5)(y + 5) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (y + 5) equal to 7.141428429 and -7.141428429.Subproblem 1
y + 5 = 7.141428429 Simplifying y + 5 = 7.141428429 Reorder the terms: 5 + y = 7.141428429 Solving 5 + y = 7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 7.141428429 + -5 Combine like terms: 5 + -5 = 0 0 + y = 7.141428429 + -5 y = 7.141428429 + -5 Combine like terms: 7.141428429 + -5 = 2.141428429 y = 2.141428429 Simplifying y = 2.141428429Subproblem 2
y + 5 = -7.141428429 Simplifying y + 5 = -7.141428429 Reorder the terms: 5 + y = -7.141428429 Solving 5 + y = -7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -7.141428429 + -5 Combine like terms: 5 + -5 = 0 0 + y = -7.141428429 + -5 y = -7.141428429 + -5 Combine like terms: -7.141428429 + -5 = -12.141428429 y = -12.141428429 Simplifying y = -12.141428429Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.141428429, -12.141428429}
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