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Simplifying 4y2 + 28y + 9 = 0 Reorder the terms: 9 + 28y + 4y2 = 0 Solving 9 + 28y + 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'. 2.25 + 7y + y2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 7y + -2.25 + y2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 7y + y2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 7y + y2 = 0 + -2.25 7y + y2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 7y + y2 = -2.25 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = -2.25 + 12.25 Reorder the terms: 12.25 + 7y + y2 = -2.25 + 12.25 Combine like terms: -2.25 + 12.25 = 10 12.25 + 7y + y2 = 10 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + 3.5) equal to 3.16227766 and -3.16227766.Subproblem 1
y + 3.5 = 3.16227766 Simplifying y + 3.5 = 3.16227766 Reorder the terms: 3.5 + y = 3.16227766 Solving 3.5 + y = 3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 3.16227766 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 3.16227766 + -3.5 y = 3.16227766 + -3.5 Combine like terms: 3.16227766 + -3.5 = -0.33772234 y = -0.33772234 Simplifying y = -0.33772234Subproblem 2
y + 3.5 = -3.16227766 Simplifying y + 3.5 = -3.16227766 Reorder the terms: 3.5 + y = -3.16227766 Solving 3.5 + y = -3.16227766 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -3.16227766 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -3.16227766 + -3.5 y = -3.16227766 + -3.5 Combine like terms: -3.16227766 + -3.5 = -6.66227766 y = -6.66227766 Simplifying y = -6.66227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.33772234, -6.66227766}
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