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Simplifying 49 + -14y + y2 = 37 Solving 49 + -14y + y2 = 37 Solving for variable 'y'. Reorder the terms: 49 + -37 + -14y + y2 = 37 + -37 Combine like terms: 49 + -37 = 12 12 + -14y + y2 = 37 + -37 Combine like terms: 37 + -37 = 0 12 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -14y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -14y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -14y + y2 = 0 + -12 -14y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -14y + y2 = -12 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 = -12 + 49 Reorder the terms: 49 + -14y + y2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + -14y + y2 = 37 Factor a perfect square on the left side: (y + -7)(y + -7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + -7) equal to 6.08276253 and -6.08276253.Subproblem 1
y + -7 = 6.08276253 Simplifying y + -7 = 6.08276253 Reorder the terms: -7 + y = 6.08276253 Solving -7 + y = 6.08276253 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 = 6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + y = 6.08276253 + 7 y = 6.08276253 + 7 Combine like terms: 6.08276253 + 7 = 13.08276253 y = 13.08276253 Simplifying y = 13.08276253Subproblem 2
y + -7 = -6.08276253 Simplifying y + -7 = -6.08276253 Reorder the terms: -7 + y = -6.08276253 Solving -7 + y = -6.08276253 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 = -6.08276253 + 7 Combine like terms: -7 + 7 = 0 0 + y = -6.08276253 + 7 y = -6.08276253 + 7 Combine like terms: -6.08276253 + 7 = 0.91723747 y = 0.91723747 Simplifying y = 0.91723747Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.08276253, 0.91723747}
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