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Simplifying (-8y)(3y + -4) + 6y + -5 = 0 Remove parenthesis around (-8y) -8y(3y + -4) + 6y + -5 = 0 Reorder the terms: -8y(-4 + 3y) + 6y + -5 = 0 (-4 * -8y + 3y * -8y) + 6y + -5 = 0 (32y + -24y2) + 6y + -5 = 0 Reorder the terms: -5 + 32y + 6y + -24y2 = 0 Combine like terms: 32y + 6y = 38y -5 + 38y + -24y2 = 0 Solving -5 + 38y + -24y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 0.2083333333 + -1.583333333y + y2 = 0 Move the constant term to the right: Add '-0.2083333333' to each side of the equation. 0.2083333333 + -1.583333333y + -0.2083333333 + y2 = 0 + -0.2083333333 Reorder the terms: 0.2083333333 + -0.2083333333 + -1.583333333y + y2 = 0 + -0.2083333333 Combine like terms: 0.2083333333 + -0.2083333333 = 0.0000000000 0.0000000000 + -1.583333333y + y2 = 0 + -0.2083333333 -1.583333333y + y2 = 0 + -0.2083333333 Combine like terms: 0 + -0.2083333333 = -0.2083333333 -1.583333333y + y2 = -0.2083333333 The y term is -1.583333333y. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333y + 0.6267361108 + y2 = -0.2083333333 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333y + y2 = -0.2083333333 + 0.6267361108 Combine like terms: -0.2083333333 + 0.6267361108 = 0.4184027775 0.6267361108 + -1.583333333y + y2 = 0.4184027775 Factor a perfect square on the left side: (y + -0.7916666665)(y + -0.7916666665) = 0.4184027775 Calculate the square root of the right side: 0.646840612 Break this problem into two subproblems by setting (y + -0.7916666665) equal to 0.646840612 and -0.646840612.Subproblem 1
y + -0.7916666665 = 0.646840612 Simplifying y + -0.7916666665 = 0.646840612 Reorder the terms: -0.7916666665 + y = 0.646840612 Solving -0.7916666665 + y = 0.646840612 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + y = 0.646840612 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + y = 0.646840612 + 0.7916666665 y = 0.646840612 + 0.7916666665 Combine like terms: 0.646840612 + 0.7916666665 = 1.4385072785 y = 1.4385072785 Simplifying y = 1.4385072785Subproblem 2
y + -0.7916666665 = -0.646840612 Simplifying y + -0.7916666665 = -0.646840612 Reorder the terms: -0.7916666665 + y = -0.646840612 Solving -0.7916666665 + y = -0.646840612 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + y = -0.646840612 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + y = -0.646840612 + 0.7916666665 y = -0.646840612 + 0.7916666665 Combine like terms: -0.646840612 + 0.7916666665 = 0.1448260545 y = 0.1448260545 Simplifying y = 0.1448260545Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4385072785, 0.1448260545}
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