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Simplifying 10y2 + 27y + -15 = 0 Reorder the terms: -15 + 27y + 10y2 = 0 Solving -15 + 27y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + 2.7y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 2.7y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 2.7y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 2.7y + y2 = 0 + 1.5 2.7y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 2.7y + y2 = 1.5 The y term is 2.7y. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7y + 1.8225 + y2 = 1.5 + 1.8225 Reorder the terms: 1.8225 + 2.7y + y2 = 1.5 + 1.8225 Combine like terms: 1.5 + 1.8225 = 3.3225 1.8225 + 2.7y + y2 = 3.3225 Factor a perfect square on the left side: (y + 1.35)(y + 1.35) = 3.3225 Calculate the square root of the right side: 1.822772613 Break this problem into two subproblems by setting (y + 1.35) equal to 1.822772613 and -1.822772613.Subproblem 1
y + 1.35 = 1.822772613 Simplifying y + 1.35 = 1.822772613 Reorder the terms: 1.35 + y = 1.822772613 Solving 1.35 + y = 1.822772613 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + y = 1.822772613 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + y = 1.822772613 + -1.35 y = 1.822772613 + -1.35 Combine like terms: 1.822772613 + -1.35 = 0.472772613 y = 0.472772613 Simplifying y = 0.472772613Subproblem 2
y + 1.35 = -1.822772613 Simplifying y + 1.35 = -1.822772613 Reorder the terms: 1.35 + y = -1.822772613 Solving 1.35 + y = -1.822772613 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + y = -1.822772613 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + y = -1.822772613 + -1.35 y = -1.822772613 + -1.35 Combine like terms: -1.822772613 + -1.35 = -3.172772613 y = -3.172772613 Simplifying y = -3.172772613Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.472772613, -3.172772613}
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