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Simplifying 10y2 + 27y + -21 = 0 Reorder the terms: -21 + 27y + 10y2 = 0 Solving -21 + 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'. -2.1 + 2.7y + y2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 2.7y + 2.1 + y2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + 2.7y + y2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 2.7y + y2 = 0 + 2.1 2.7y + y2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 2.7y + y2 = 2.1 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 = 2.1 + 1.8225 Reorder the terms: 1.8225 + 2.7y + y2 = 2.1 + 1.8225 Combine like terms: 2.1 + 1.8225 = 3.9225 1.8225 + 2.7y + y2 = 3.9225 Factor a perfect square on the left side: (y + 1.35)(y + 1.35) = 3.9225 Calculate the square root of the right side: 1.980530232 Break this problem into two subproblems by setting (y + 1.35) equal to 1.980530232 and -1.980530232.Subproblem 1
y + 1.35 = 1.980530232 Simplifying y + 1.35 = 1.980530232 Reorder the terms: 1.35 + y = 1.980530232 Solving 1.35 + y = 1.980530232 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 = 1.980530232 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + y = 1.980530232 + -1.35 y = 1.980530232 + -1.35 Combine like terms: 1.980530232 + -1.35 = 0.630530232 y = 0.630530232 Simplifying y = 0.630530232Subproblem 2
y + 1.35 = -1.980530232 Simplifying y + 1.35 = -1.980530232 Reorder the terms: 1.35 + y = -1.980530232 Solving 1.35 + y = -1.980530232 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 = -1.980530232 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + y = -1.980530232 + -1.35 y = -1.980530232 + -1.35 Combine like terms: -1.980530232 + -1.35 = -3.330530232 y = -3.330530232 Simplifying y = -3.330530232Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.630530232, -3.330530232}
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