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Simplifying -4y2 + -28y + 5 = 0 Reorder the terms: 5 + -28y + -4y2 = 0 Solving 5 + -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'. -1.25 + 7y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 7y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 7y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 7y + y2 = 0 + 1.25 7y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 7y + y2 = 1.25 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 = 1.25 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 1.25 + 12.25 Combine like terms: 1.25 + 12.25 = 13.5 12.25 + 7y + y2 = 13.5 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (y + 3.5) equal to 3.674234614 and -3.674234614.Subproblem 1
y + 3.5 = 3.674234614 Simplifying y + 3.5 = 3.674234614 Reorder the terms: 3.5 + y = 3.674234614 Solving 3.5 + y = 3.674234614 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 = 3.674234614 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 3.674234614 + -3.5 y = 3.674234614 + -3.5 Combine like terms: 3.674234614 + -3.5 = 0.174234614 y = 0.174234614 Simplifying y = 0.174234614Subproblem 2
y + 3.5 = -3.674234614 Simplifying y + 3.5 = -3.674234614 Reorder the terms: 3.5 + y = -3.674234614 Solving 3.5 + y = -3.674234614 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 = -3.674234614 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -3.674234614 + -3.5 y = -3.674234614 + -3.5 Combine like terms: -3.674234614 + -3.5 = -7.174234614 y = -7.174234614 Simplifying y = -7.174234614Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.174234614, -7.174234614}
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