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Simplifying 6 + -1(4y + -7) * y = 5 Reorder the terms: 6 + -1(-7 + 4y) * y = 5 Reorder the terms for easier multiplication: 6 + -1y(-7 + 4y) = 5 6 + (-7 * -1y + 4y * -1y) = 5 6 + (7y + -4y2) = 5 Solving 6 + 7y + -4y2 = 5 Solving for variable 'y'. Reorder the terms: 6 + -5 + 7y + -4y2 = 5 + -5 Combine like terms: 6 + -5 = 1 1 + 7y + -4y2 = 5 + -5 Combine like terms: 5 + -5 = 0 1 + 7y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -1.75y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.75y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.75y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.75y + y2 = 0 + 0.25 -1.75y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.75y + y2 = 0.25 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 = 0.25 + 0.765625 Reorder the terms: 0.765625 + -1.75y + y2 = 0.25 + 0.765625 Combine like terms: 0.25 + 0.765625 = 1.015625 0.765625 + -1.75y + y2 = 1.015625 Factor a perfect square on the left side: (y + -0.875)(y + -0.875) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (y + -0.875) equal to 1.007782219 and -1.007782219.Subproblem 1
y + -0.875 = 1.007782219 Simplifying y + -0.875 = 1.007782219 Reorder the terms: -0.875 + y = 1.007782219 Solving -0.875 + y = 1.007782219 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 = 1.007782219 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + y = 1.007782219 + 0.875 y = 1.007782219 + 0.875 Combine like terms: 1.007782219 + 0.875 = 1.882782219 y = 1.882782219 Simplifying y = 1.882782219Subproblem 2
y + -0.875 = -1.007782219 Simplifying y + -0.875 = -1.007782219 Reorder the terms: -0.875 + y = -1.007782219 Solving -0.875 + y = -1.007782219 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 = -1.007782219 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + y = -1.007782219 + 0.875 y = -1.007782219 + 0.875 Combine like terms: -1.007782219 + 0.875 = -0.132782219 y = -0.132782219 Simplifying y = -0.132782219Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.882782219, -0.132782219}
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