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Simplifying y(y + -14) + 4(y + -18) = 0 Reorder the terms: y(-14 + y) + 4(y + -18) = 0 (-14 * y + y * y) + 4(y + -18) = 0 (-14y + y2) + 4(y + -18) = 0 Reorder the terms: -14y + y2 + 4(-18 + y) = 0 -14y + y2 + (-18 * 4 + y * 4) = 0 -14y + y2 + (-72 + 4y) = 0 Reorder the terms: -72 + -14y + 4y + y2 = 0 Combine like terms: -14y + 4y = -10y -72 + -10y + y2 = 0 Solving -72 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -10y + 72 + y2 = 0 + 72 Reorder the terms: -72 + 72 + -10y + y2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -10y + y2 = 0 + 72 -10y + y2 = 0 + 72 Combine like terms: 0 + 72 = 72 -10y + y2 = 72 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 = 72 + 25 Reorder the terms: 25 + -10y + y2 = 72 + 25 Combine like terms: 72 + 25 = 97 25 + -10y + y2 = 97 Factor a perfect square on the left side: (y + -5)(y + -5) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (y + -5) equal to 9.848857802 and -9.848857802.Subproblem 1
y + -5 = 9.848857802 Simplifying y + -5 = 9.848857802 Reorder the terms: -5 + y = 9.848857802 Solving -5 + y = 9.848857802 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 = 9.848857802 + 5 Combine like terms: -5 + 5 = 0 0 + y = 9.848857802 + 5 y = 9.848857802 + 5 Combine like terms: 9.848857802 + 5 = 14.848857802 y = 14.848857802 Simplifying y = 14.848857802Subproblem 2
y + -5 = -9.848857802 Simplifying y + -5 = -9.848857802 Reorder the terms: -5 + y = -9.848857802 Solving -5 + y = -9.848857802 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 = -9.848857802 + 5 Combine like terms: -5 + 5 = 0 0 + y = -9.848857802 + 5 y = -9.848857802 + 5 Combine like terms: -9.848857802 + 5 = -4.848857802 y = -4.848857802 Simplifying y = -4.848857802Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.848857802, -4.848857802}
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