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Simplifying 5 = (y2) + -1(8y) 5 = y2 + -1(8y) Remove parenthesis around (8y) 5 = y2 + -1 * 8y Multiply -1 * 8 5 = y2 + -8y Reorder the terms: 5 = -8y + y2 Solving 5 = -8y + y2 Solving for variable 'y'. Reorder the terms: 5 + 8y + -1y2 = -8y + 8y + y2 + -1y2 Combine like terms: -8y + 8y = 0 5 + 8y + -1y2 = 0 + y2 + -1y2 5 + 8y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 5 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -8y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -8y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8y + y2 = 0 + 5 -8y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8y + y2 = 5 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 5 + 16 Reorder the terms: 16 + -8y + y2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + -8y + y2 = 21 Factor a perfect square on the left side: (y + -4)(y + -4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + -4) equal to 4.582575695 and -4.582575695.Subproblem 1
y + -4 = 4.582575695 Simplifying y + -4 = 4.582575695 Reorder the terms: -4 + y = 4.582575695 Solving -4 + y = 4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.582575695 + 4 y = 4.582575695 + 4 Combine like terms: 4.582575695 + 4 = 8.582575695 y = 8.582575695 Simplifying y = 8.582575695Subproblem 2
y + -4 = -4.582575695 Simplifying y + -4 = -4.582575695 Reorder the terms: -4 + y = -4.582575695 Solving -4 + y = -4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -4.582575695 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.582575695 + 4 y = -4.582575695 + 4 Combine like terms: -4.582575695 + 4 = -0.582575695 y = -0.582575695 Simplifying y = -0.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.582575695, -0.582575695}
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