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Simplifying 4y2 + 7y + -3 = 0 Reorder the terms: -3 + 7y + 4y2 = 0 Solving -3 + 7y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 1.75y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.75y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.75y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.75y + y2 = 0 + 0.75 1.75y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.75y + y2 = 0.75 The y term is 1.75y. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75y + 0.765625 + y2 = 0.75 + 0.765625 Reorder the terms: 0.765625 + 1.75y + y2 = 0.75 + 0.765625 Combine like terms: 0.75 + 0.765625 = 1.515625 0.765625 + 1.75y + y2 = 1.515625 Factor a perfect square on the left side: (y + 0.875)(y + 0.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (y + 0.875) equal to 1.231107225 and -1.231107225.Subproblem 1
y + 0.875 = 1.231107225 Simplifying y + 0.875 = 1.231107225 Reorder the terms: 0.875 + y = 1.231107225 Solving 0.875 + y = 1.231107225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = 1.231107225 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = 1.231107225 + -0.875 y = 1.231107225 + -0.875 Combine like terms: 1.231107225 + -0.875 = 0.356107225 y = 0.356107225 Simplifying y = 0.356107225Subproblem 2
y + 0.875 = -1.231107225 Simplifying y + 0.875 = -1.231107225 Reorder the terms: 0.875 + y = -1.231107225 Solving 0.875 + y = -1.231107225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = -1.231107225 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = -1.231107225 + -0.875 y = -1.231107225 + -0.875 Combine like terms: -1.231107225 + -0.875 = -2.106107225 y = -2.106107225 Simplifying y = -2.106107225Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.356107225, -2.106107225}
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