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Simplifying y(8y + -7) = 3 Reorder the terms: y(-7 + 8y) = 3 (-7 * y + 8y * y) = 3 (-7y + 8y2) = 3 Solving -7y + 8y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + -7y + 8y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -7y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.875y + y2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.875y + 0.375 + y2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.875y + y2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.875y + y2 = 0 + 0.375 -0.875y + y2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.875y + y2 = 0.375 The y term is -0.875y. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875y + 0.19140625 + y2 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + -0.875y + y2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + -0.875y + y2 = 0.56640625 Factor a perfect square on the left side: (y + -0.4375)(y + -0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (y + -0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
y + -0.4375 = 0.752599661 Simplifying y + -0.4375 = 0.752599661 Reorder the terms: -0.4375 + y = 0.752599661 Solving -0.4375 + y = 0.752599661 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = 0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = 0.752599661 + 0.4375 y = 0.752599661 + 0.4375 Combine like terms: 0.752599661 + 0.4375 = 1.190099661 y = 1.190099661 Simplifying y = 1.190099661Subproblem 2
y + -0.4375 = -0.752599661 Simplifying y + -0.4375 = -0.752599661 Reorder the terms: -0.4375 + y = -0.752599661 Solving -0.4375 + y = -0.752599661 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = -0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = -0.752599661 + 0.4375 y = -0.752599661 + 0.4375 Combine like terms: -0.752599661 + 0.4375 = -0.315099661 y = -0.315099661 Simplifying y = -0.315099661Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.190099661, -0.315099661}
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