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Simplifying 5y2 + -7y + -9 = 0 Reorder the terms: -9 + -7y + 5y2 = 0 Solving -9 + -7y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -1.4y + y2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.4y + 1.8 + y2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.4y + y2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.4y + y2 = 0 + 1.8 -1.4y + y2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.4y + y2 = 1.8 The y term is -1.4y. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y + 0.49 + y2 = 1.8 + 0.49 Reorder the terms: 0.49 + -1.4y + y2 = 1.8 + 0.49 Combine like terms: 1.8 + 0.49 = 2.29 0.49 + -1.4y + y2 = 2.29 Factor a perfect square on the left side: (y + -0.7)(y + -0.7) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (y + -0.7) equal to 1.513274595 and -1.513274595.Subproblem 1
y + -0.7 = 1.513274595 Simplifying y + -0.7 = 1.513274595 Reorder the terms: -0.7 + y = 1.513274595 Solving -0.7 + y = 1.513274595 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = 1.513274595 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = 1.513274595 + 0.7 y = 1.513274595 + 0.7 Combine like terms: 1.513274595 + 0.7 = 2.213274595 y = 2.213274595 Simplifying y = 2.213274595Subproblem 2
y + -0.7 = -1.513274595 Simplifying y + -0.7 = -1.513274595 Reorder the terms: -0.7 + y = -1.513274595 Solving -0.7 + y = -1.513274595 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + y = -1.513274595 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + y = -1.513274595 + 0.7 y = -1.513274595 + 0.7 Combine like terms: -1.513274595 + 0.7 = -0.813274595 y = -0.813274595 Simplifying y = -0.813274595Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.213274595, -0.813274595}
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