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Simplifying 4y2 + 56y + 49 = 0 Reorder the terms: 49 + 56y + 4y2 = 0 Solving 49 + 56y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + 14y + y2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 14y + -12.25 + y2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 14y + y2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 14y + y2 = 0 + -12.25 14y + y2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 14y + y2 = -12.25 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 = -12.25 + 49 Reorder the terms: 49 + 14y + y2 = -12.25 + 49 Combine like terms: -12.25 + 49 = 36.75 49 + 14y + y2 = 36.75 Factor a perfect square on the left side: (y + 7)(y + 7) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (y + 7) equal to 6.062177826 and -6.062177826.Subproblem 1
y + 7 = 6.062177826 Simplifying y + 7 = 6.062177826 Reorder the terms: 7 + y = 6.062177826 Solving 7 + y = 6.062177826 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 = 6.062177826 + -7 Combine like terms: 7 + -7 = 0 0 + y = 6.062177826 + -7 y = 6.062177826 + -7 Combine like terms: 6.062177826 + -7 = -0.937822174 y = -0.937822174 Simplifying y = -0.937822174Subproblem 2
y + 7 = -6.062177826 Simplifying y + 7 = -6.062177826 Reorder the terms: 7 + y = -6.062177826 Solving 7 + y = -6.062177826 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 = -6.062177826 + -7 Combine like terms: 7 + -7 = 0 0 + y = -6.062177826 + -7 y = -6.062177826 + -7 Combine like terms: -6.062177826 + -7 = -13.062177826 y = -13.062177826 Simplifying y = -13.062177826Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.937822174, -13.062177826}
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