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Simplifying -7y2(8y2 + 8y + -9) = 0 Reorder the terms: -7y2(-9 + 8y + 8y2) = 0 (-9 * -7y2 + 8y * -7y2 + 8y2 * -7y2) = 0 (63y2 + -56y3 + -56y4) = 0 Solving 63y2 + -56y3 + -56y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7y2'. 7y2(9 + -8y + -8y2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(9 + -8y + -8y2)' equal to zero and attempt to solve: Simplifying 9 + -8y + -8y2 = 0 Solving 9 + -8y + -8y2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + y + y2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + y + 1.125 + y2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + y + y2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y + y2 = 0 + 1.125 y + y2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 y + y2 = 1.125 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y2 = 1.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 1.125 + 0.25 Combine like terms: 1.125 + 0.25 = 1.375 1.25 + y2 = 1.375 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting (y + 0.5) equal to 1.17260394 and -1.17260394.Subproblem 1
y + 0.5 = 1.17260394 Simplifying y + 0.5 = 1.17260394 Reorder the terms: 0.5 + y = 1.17260394 Solving 0.5 + y = 1.17260394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.17260394 + -0.5 y = 1.17260394 + -0.5 Combine like terms: 1.17260394 + -0.5 = 0.67260394 y = 0.67260394 Simplifying y = 0.67260394Subproblem 2
y + 0.5 = -1.17260394 Simplifying y + 0.5 = -1.17260394 Reorder the terms: 0.5 + y = -1.17260394 Solving 0.5 + y = -1.17260394 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.17260394 + -0.5 y = -1.17260394 + -0.5 Combine like terms: -1.17260394 + -0.5 = -1.67260394 y = -1.67260394 Simplifying y = -1.67260394Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.67260394, -1.67260394}Solution
y = {0, 0.67260394, -1.67260394}
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