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Simplifying y2 + -14y = -26 Reorder the terms: -14y + y2 = -26 Solving -14y + y2 = -26 Solving for variable 'y'. Reorder the terms: 26 + -14y + y2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -14y + -26 + y2 = 0 + -26 Reorder the terms: 26 + -26 + -14y + y2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -14y + y2 = 0 + -26 -14y + y2 = 0 + -26 Combine like terms: 0 + -26 = -26 -14y + y2 = -26 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -26 + 49 Reorder the terms: 49 + -14y + y2 = -26 + 49 Combine like terms: -26 + 49 = 23 49 + -14y + y2 = 23 Factor a perfect square on the left side: (y + -7)(y + -7) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (y + -7) equal to 4.795831523 and -4.795831523.Subproblem 1
y + -7 = 4.795831523 Simplifying y + -7 = 4.795831523 Reorder the terms: -7 + y = 4.795831523 Solving -7 + y = 4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 4.795831523 + 7 Combine like terms: -7 + 7 = 0 0 + y = 4.795831523 + 7 y = 4.795831523 + 7 Combine like terms: 4.795831523 + 7 = 11.795831523 y = 11.795831523 Simplifying y = 11.795831523Subproblem 2
y + -7 = -4.795831523 Simplifying y + -7 = -4.795831523 Reorder the terms: -7 + y = -4.795831523 Solving -7 + y = -4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -4.795831523 + 7 Combine like terms: -7 + 7 = 0 0 + y = -4.795831523 + 7 y = -4.795831523 + 7 Combine like terms: -4.795831523 + 7 = 2.204168477 y = 2.204168477 Simplifying y = 2.204168477Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.795831523, 2.204168477}
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