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Simplifying (6y2 + -7y + -5) + (2y2 + -4y + 3) = 0 Reorder the terms: (-5 + -7y + 6y2) + (2y2 + -4y + 3) = 0 Remove parenthesis around (-5 + -7y + 6y2) -5 + -7y + 6y2 + (2y2 + -4y + 3) = 0 Reorder the terms: -5 + -7y + 6y2 + (3 + -4y + 2y2) = 0 Remove parenthesis around (3 + -4y + 2y2) -5 + -7y + 6y2 + 3 + -4y + 2y2 = 0 Reorder the terms: -5 + 3 + -7y + -4y + 6y2 + 2y2 = 0 Combine like terms: -5 + 3 = -2 -2 + -7y + -4y + 6y2 + 2y2 = 0 Combine like terms: -7y + -4y = -11y -2 + -11y + 6y2 + 2y2 = 0 Combine like terms: 6y2 + 2y2 = 8y2 -2 + -11y + 8y2 = 0 Solving -2 + -11y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -1.375y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.375y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.375y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.375y + y2 = 0 + 0.25 -1.375y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.375y + y2 = 0.25 The y term is -1.375y. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375y + 0.47265625 + y2 = 0.25 + 0.47265625 Reorder the terms: 0.47265625 + -1.375y + y2 = 0.25 + 0.47265625 Combine like terms: 0.25 + 0.47265625 = 0.72265625 0.47265625 + -1.375y + y2 = 0.72265625 Factor a perfect square on the left side: (y + -0.6875)(y + -0.6875) = 0.72265625 Calculate the square root of the right side: 0.850091907 Break this problem into two subproblems by setting (y + -0.6875) equal to 0.850091907 and -0.850091907.Subproblem 1
y + -0.6875 = 0.850091907 Simplifying y + -0.6875 = 0.850091907 Reorder the terms: -0.6875 + y = 0.850091907 Solving -0.6875 + y = 0.850091907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + y = 0.850091907 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + y = 0.850091907 + 0.6875 y = 0.850091907 + 0.6875 Combine like terms: 0.850091907 + 0.6875 = 1.537591907 y = 1.537591907 Simplifying y = 1.537591907Subproblem 2
y + -0.6875 = -0.850091907 Simplifying y + -0.6875 = -0.850091907 Reorder the terms: -0.6875 + y = -0.850091907 Solving -0.6875 + y = -0.850091907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + y = -0.850091907 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + y = -0.850091907 + 0.6875 y = -0.850091907 + 0.6875 Combine like terms: -0.850091907 + 0.6875 = -0.162591907 y = -0.162591907 Simplifying y = -0.162591907Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.537591907, -0.162591907}
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