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Simplifying y2 + -10y + 4 = 0 Reorder the terms: 4 + -10y + y2 = 0 Solving 4 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -10y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10y + y2 = 0 + -4 -10y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10y + y2 = -4 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 = -4 + 25 Reorder the terms: 25 + -10y + y2 = -4 + 25 Combine like terms: -4 + 25 = 21 25 + -10y + y2 = 21 Factor a perfect square on the left side: (y + -5)(y + -5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + -5) equal to 4.582575695 and -4.582575695.Subproblem 1
y + -5 = 4.582575695 Simplifying y + -5 = 4.582575695 Reorder the terms: -5 + y = 4.582575695 Solving -5 + y = 4.582575695 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 = 4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.582575695 + 5 y = 4.582575695 + 5 Combine like terms: 4.582575695 + 5 = 9.582575695 y = 9.582575695 Simplifying y = 9.582575695Subproblem 2
y + -5 = -4.582575695 Simplifying y + -5 = -4.582575695 Reorder the terms: -5 + y = -4.582575695 Solving -5 + y = -4.582575695 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 = -4.582575695 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.582575695 + 5 y = -4.582575695 + 5 Combine like terms: -4.582575695 + 5 = 0.417424305 y = 0.417424305 Simplifying y = 0.417424305Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.582575695, 0.417424305}
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