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Simplifying 25y2 + -65y + -384 = 0 Reorder the terms: -384 + -65y + 25y2 = 0 Solving -384 + -65y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -15.36 + -2.6y + y2 = 0 Move the constant term to the right: Add '15.36' to each side of the equation. -15.36 + -2.6y + 15.36 + y2 = 0 + 15.36 Reorder the terms: -15.36 + 15.36 + -2.6y + y2 = 0 + 15.36 Combine like terms: -15.36 + 15.36 = 0.00 0.00 + -2.6y + y2 = 0 + 15.36 -2.6y + y2 = 0 + 15.36 Combine like terms: 0 + 15.36 = 15.36 -2.6y + y2 = 15.36 The y term is -2.6y. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6y + 1.69 + y2 = 15.36 + 1.69 Reorder the terms: 1.69 + -2.6y + y2 = 15.36 + 1.69 Combine like terms: 15.36 + 1.69 = 17.05 1.69 + -2.6y + y2 = 17.05 Factor a perfect square on the left side: (y + -1.3)(y + -1.3) = 17.05 Calculate the square root of the right side: 4.129164564 Break this problem into two subproblems by setting (y + -1.3) equal to 4.129164564 and -4.129164564.Subproblem 1
y + -1.3 = 4.129164564 Simplifying y + -1.3 = 4.129164564 Reorder the terms: -1.3 + y = 4.129164564 Solving -1.3 + y = 4.129164564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = 4.129164564 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = 4.129164564 + 1.3 y = 4.129164564 + 1.3 Combine like terms: 4.129164564 + 1.3 = 5.429164564 y = 5.429164564 Simplifying y = 5.429164564Subproblem 2
y + -1.3 = -4.129164564 Simplifying y + -1.3 = -4.129164564 Reorder the terms: -1.3 + y = -4.129164564 Solving -1.3 + y = -4.129164564 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + y = -4.129164564 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + y = -4.129164564 + 1.3 y = -4.129164564 + 1.3 Combine like terms: -4.129164564 + 1.3 = -2.829164564 y = -2.829164564 Simplifying y = -2.829164564Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.429164564, -2.829164564}
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