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Simplifying 4y2 + 28y + -27 = 0 Reorder the terms: -27 + 28y + 4y2 = 0 Solving -27 + 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'. -6.75 + 7y + y2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 7y + 6.75 + y2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 7y + y2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 7y + y2 = 0 + 6.75 7y + y2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 7y + y2 = 6.75 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 = 6.75 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 6.75 + 12.25 Combine like terms: 6.75 + 12.25 = 19 12.25 + 7y + y2 = 19 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + 3.5) equal to 4.358898944 and -4.358898944.Subproblem 1
y + 3.5 = 4.358898944 Simplifying y + 3.5 = 4.358898944 Reorder the terms: 3.5 + y = 4.358898944 Solving 3.5 + y = 4.358898944 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 = 4.358898944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 4.358898944 + -3.5 y = 4.358898944 + -3.5 Combine like terms: 4.358898944 + -3.5 = 0.858898944 y = 0.858898944 Simplifying y = 0.858898944Subproblem 2
y + 3.5 = -4.358898944 Simplifying y + 3.5 = -4.358898944 Reorder the terms: 3.5 + y = -4.358898944 Solving 3.5 + y = -4.358898944 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 = -4.358898944 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -4.358898944 + -3.5 y = -4.358898944 + -3.5 Combine like terms: -4.358898944 + -3.5 = -7.858898944 y = -7.858898944 Simplifying y = -7.858898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.858898944, -7.858898944}
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