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Simplifying 5y2 + 7y + -4 = 0 Reorder the terms: -4 + 7y + 5y2 = 0 Solving -4 + 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'. -0.8 + 1.4y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 1.4y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 1.4y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 1.4y + y2 = 0 + 0.8 1.4y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 1.4y + y2 = 0.8 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 = 0.8 + 0.49 Reorder the terms: 0.49 + 1.4y + y2 = 0.8 + 0.49 Combine like terms: 0.8 + 0.49 = 1.29 0.49 + 1.4y + y2 = 1.29 Factor a perfect square on the left side: (y + 0.7)(y + 0.7) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (y + 0.7) equal to 1.135781669 and -1.135781669.Subproblem 1
y + 0.7 = 1.135781669 Simplifying y + 0.7 = 1.135781669 Reorder the terms: 0.7 + y = 1.135781669 Solving 0.7 + y = 1.135781669 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 = 1.135781669 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = 1.135781669 + -0.7 y = 1.135781669 + -0.7 Combine like terms: 1.135781669 + -0.7 = 0.435781669 y = 0.435781669 Simplifying y = 0.435781669Subproblem 2
y + 0.7 = -1.135781669 Simplifying y + 0.7 = -1.135781669 Reorder the terms: 0.7 + y = -1.135781669 Solving 0.7 + y = -1.135781669 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 = -1.135781669 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = -1.135781669 + -0.7 y = -1.135781669 + -0.7 Combine like terms: -1.135781669 + -0.7 = -1.835781669 y = -1.835781669 Simplifying y = -1.835781669Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.435781669, -1.835781669}
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