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Simplifying -4y(y + 7) = -3y + -2 Reorder the terms: -4y(7 + y) = -3y + -2 (7 * -4y + y * -4y) = -3y + -2 (-28y + -4y2) = -3y + -2 Reorder the terms: -28y + -4y2 = -2 + -3y Solving -28y + -4y2 = -2 + -3y Solving for variable 'y'. Reorder the terms: 2 + -28y + 3y + -4y2 = -2 + -3y + 2 + 3y Combine like terms: -28y + 3y = -25y 2 + -25y + -4y2 = -2 + -3y + 2 + 3y Reorder the terms: 2 + -25y + -4y2 = -2 + 2 + -3y + 3y Combine like terms: -2 + 2 = 0 2 + -25y + -4y2 = 0 + -3y + 3y 2 + -25y + -4y2 = -3y + 3y Combine like terms: -3y + 3y = 0 2 + -25y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 6.25y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 6.25y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 6.25y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 6.25y + y2 = 0 + 0.5 6.25y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 6.25y + y2 = 0.5 The y term is 6.25y. Take half its coefficient (3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. 6.25y + 9.765625 + y2 = 0.5 + 9.765625 Reorder the terms: 9.765625 + 6.25y + y2 = 0.5 + 9.765625 Combine like terms: 0.5 + 9.765625 = 10.265625 9.765625 + 6.25y + y2 = 10.265625 Factor a perfect square on the left side: (y + 3.125)(y + 3.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (y + 3.125) equal to 3.204001404 and -3.204001404.Subproblem 1
y + 3.125 = 3.204001404 Simplifying y + 3.125 = 3.204001404 Reorder the terms: 3.125 + y = 3.204001404 Solving 3.125 + y = 3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + y = 3.204001404 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + y = 3.204001404 + -3.125 y = 3.204001404 + -3.125 Combine like terms: 3.204001404 + -3.125 = 0.079001404 y = 0.079001404 Simplifying y = 0.079001404Subproblem 2
y + 3.125 = -3.204001404 Simplifying y + 3.125 = -3.204001404 Reorder the terms: 3.125 + y = -3.204001404 Solving 3.125 + y = -3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + y = -3.204001404 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + y = -3.204001404 + -3.125 y = -3.204001404 + -3.125 Combine like terms: -3.204001404 + -3.125 = -6.329001404 y = -6.329001404 Simplifying y = -6.329001404Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.079001404, -6.329001404}
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