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Simplifying 4(8y2 + -7y + 4) + -2(8y2 + -2y + 9) = 0 Reorder the terms: 4(4 + -7y + 8y2) + -2(8y2 + -2y + 9) = 0 (4 * 4 + -7y * 4 + 8y2 * 4) + -2(8y2 + -2y + 9) = 0 (16 + -28y + 32y2) + -2(8y2 + -2y + 9) = 0 Reorder the terms: 16 + -28y + 32y2 + -2(9 + -2y + 8y2) = 0 16 + -28y + 32y2 + (9 * -2 + -2y * -2 + 8y2 * -2) = 0 16 + -28y + 32y2 + (-18 + 4y + -16y2) = 0 Reorder the terms: 16 + -18 + -28y + 4y + 32y2 + -16y2 = 0 Combine like terms: 16 + -18 = -2 -2 + -28y + 4y + 32y2 + -16y2 = 0 Combine like terms: -28y + 4y = -24y -2 + -24y + 32y2 + -16y2 = 0 Combine like terms: 32y2 + -16y2 = 16y2 -2 + -24y + 16y2 = 0 Solving -2 + -24y + 16y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -12y + 8y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -12y + 8y2)' equal to zero and attempt to solve: Simplifying -1 + -12y + 8y2 = 0 Solving -1 + -12y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -1.5y + y2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -1.5y + 0.125 + y2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -1.5y + y2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -1.5y + y2 = 0 + 0.125 -1.5y + y2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -1.5y + y2 = 0.125 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 0.125 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 0.125 + 0.5625 Combine like terms: 0.125 + 0.5625 = 0.6875 0.5625 + -1.5y + y2 = 0.6875 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 0.6875 Calculate the square root of the right side: 0.829156198 Break this problem into two subproblems by setting (y + -0.75) equal to 0.829156198 and -0.829156198.Subproblem 1
y + -0.75 = 0.829156198 Simplifying y + -0.75 = 0.829156198 Reorder the terms: -0.75 + y = 0.829156198 Solving -0.75 + y = 0.829156198 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 0.829156198 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 0.829156198 + 0.75 y = 0.829156198 + 0.75 Combine like terms: 0.829156198 + 0.75 = 1.579156198 y = 1.579156198 Simplifying y = 1.579156198Subproblem 2
y + -0.75 = -0.829156198 Simplifying y + -0.75 = -0.829156198 Reorder the terms: -0.75 + y = -0.829156198 Solving -0.75 + y = -0.829156198 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -0.829156198 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -0.829156198 + 0.75 y = -0.829156198 + 0.75 Combine like terms: -0.829156198 + 0.75 = -0.079156198 y = -0.079156198 Simplifying y = -0.079156198Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.579156198, -0.079156198}Solution
y = {1.579156198, -0.079156198}
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