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Simplifying -4y2 + 25y + 28 = 0 Reorder the terms: 28 + 25y + -4y2 = 0 Solving 28 + 25y + -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'. -7 + -6.25y + y2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.25y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -6.25y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.25y + y2 = 0 + 7 -6.25y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.25y + y2 = 7 The y term is -6.25y. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25y + 9.765625 + y2 = 7 + 9.765625 Reorder the terms: 9.765625 + -6.25y + y2 = 7 + 9.765625 Combine like terms: 7 + 9.765625 = 16.765625 9.765625 + -6.25y + y2 = 16.765625 Factor a perfect square on the left side: (y + -3.125)(y + -3.125) = 16.765625 Calculate the square root of the right side: 4.094584839 Break this problem into two subproblems by setting (y + -3.125) equal to 4.094584839 and -4.094584839.Subproblem 1
y + -3.125 = 4.094584839 Simplifying y + -3.125 = 4.094584839 Reorder the terms: -3.125 + y = 4.094584839 Solving -3.125 + y = 4.094584839 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + y = 4.094584839 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + y = 4.094584839 + 3.125 y = 4.094584839 + 3.125 Combine like terms: 4.094584839 + 3.125 = 7.219584839 y = 7.219584839 Simplifying y = 7.219584839Subproblem 2
y + -3.125 = -4.094584839 Simplifying y + -3.125 = -4.094584839 Reorder the terms: -3.125 + y = -4.094584839 Solving -3.125 + y = -4.094584839 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + y = -4.094584839 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + y = -4.094584839 + 3.125 y = -4.094584839 + 3.125 Combine like terms: -4.094584839 + 3.125 = -0.969584839 y = -0.969584839 Simplifying y = -0.969584839Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.219584839, -0.969584839}
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