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Simplifying y2 + 7y = 104 Reorder the terms: 7y + y2 = 104 Solving 7y + y2 = 104 Solving for variable 'y'. Reorder the terms: -104 + 7y + y2 = 104 + -104 Combine like terms: 104 + -104 = 0 -104 + 7y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 7y + 104 + y2 = 0 + 104 Reorder the terms: -104 + 104 + 7y + y2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 7y + y2 = 0 + 104 7y + y2 = 0 + 104 Combine like terms: 0 + 104 = 104 7y + y2 = 104 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 = 104 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 104 + 12.25 Combine like terms: 104 + 12.25 = 116.25 12.25 + 7y + y2 = 116.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (y + 3.5) equal to 10.781929326 and -10.781929326.Subproblem 1
y + 3.5 = 10.781929326 Simplifying y + 3.5 = 10.781929326 Reorder the terms: 3.5 + y = 10.781929326 Solving 3.5 + y = 10.781929326 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 = 10.781929326 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 10.781929326 + -3.5 y = 10.781929326 + -3.5 Combine like terms: 10.781929326 + -3.5 = 7.281929326 y = 7.281929326 Simplifying y = 7.281929326Subproblem 2
y + 3.5 = -10.781929326 Simplifying y + 3.5 = -10.781929326 Reorder the terms: 3.5 + y = -10.781929326 Solving 3.5 + y = -10.781929326 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 = -10.781929326 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -10.781929326 + -3.5 y = -10.781929326 + -3.5 Combine like terms: -10.781929326 + -3.5 = -14.281929326 y = -14.281929326 Simplifying y = -14.281929326Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.281929326, -14.281929326}
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