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Simplifying -1y2(5y2 + 7y + -8) = 0 Reorder the terms: -1y2(-8 + 7y + 5y2) = 0 (-8 * -1y2 + 7y * -1y2 + 5y2 * -1y2) = 0 (8y2 + -7y3 + -5y4) = 0 Solving 8y2 + -7y3 + -5y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y2'. y2(8 + -7y + -5y2) = 0Subproblem 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 '(8 + -7y + -5y2)' equal to zero and attempt to solve: Simplifying 8 + -7y + -5y2 = 0 Solving 8 + -7y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + 1.4y + y2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 1.4y + 1.6 + y2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 1.4y + y2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 1.4y + y2 = 0 + 1.6 1.4y + y2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 1.4y + y2 = 1.6 The y term is 1.4y. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4y + 0.49 + y2 = 1.6 + 0.49 Reorder the terms: 0.49 + 1.4y + y2 = 1.6 + 0.49 Combine like terms: 1.6 + 0.49 = 2.09 0.49 + 1.4y + y2 = 2.09 Factor a perfect square on the left side: (y + 0.7)(y + 0.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (y + 0.7) equal to 1.445683229 and -1.445683229.Subproblem 1
y + 0.7 = 1.445683229 Simplifying y + 0.7 = 1.445683229 Reorder the terms: 0.7 + y = 1.445683229 Solving 0.7 + y = 1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + y = 1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = 1.445683229 + -0.7 y = 1.445683229 + -0.7 Combine like terms: 1.445683229 + -0.7 = 0.745683229 y = 0.745683229 Simplifying y = 0.745683229Subproblem 2
y + 0.7 = -1.445683229 Simplifying y + 0.7 = -1.445683229 Reorder the terms: 0.7 + y = -1.445683229 Solving 0.7 + y = -1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + y = -1.445683229 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = -1.445683229 + -0.7 y = -1.445683229 + -0.7 Combine like terms: -1.445683229 + -0.7 = -2.145683229 y = -2.145683229 Simplifying y = -2.145683229Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.745683229, -2.145683229}Solution
y = {0, 0.745683229, -2.145683229}
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