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Simplifying y2 + -14y + 43 = 0 Reorder the terms: 43 + -14y + y2 = 0 Solving 43 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -14y + -43 + y2 = 0 + -43 Reorder the terms: 43 + -43 + -14y + y2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -14y + y2 = 0 + -43 -14y + y2 = 0 + -43 Combine like terms: 0 + -43 = -43 -14y + y2 = -43 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 = -43 + 49 Reorder the terms: 49 + -14y + y2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + -14y + y2 = 6 Factor a perfect square on the left side: (y + -7)(y + -7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (y + -7) equal to 2.449489743 and -2.449489743.Subproblem 1
y + -7 = 2.449489743 Simplifying y + -7 = 2.449489743 Reorder the terms: -7 + y = 2.449489743 Solving -7 + y = 2.449489743 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 = 2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + y = 2.449489743 + 7 y = 2.449489743 + 7 Combine like terms: 2.449489743 + 7 = 9.449489743 y = 9.449489743 Simplifying y = 9.449489743Subproblem 2
y + -7 = -2.449489743 Simplifying y + -7 = -2.449489743 Reorder the terms: -7 + y = -2.449489743 Solving -7 + y = -2.449489743 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 = -2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + y = -2.449489743 + 7 y = -2.449489743 + 7 Combine like terms: -2.449489743 + 7 = 4.550510257 y = 4.550510257 Simplifying y = 4.550510257Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.449489743, 4.550510257}
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