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Simplifying 30y + 42y2 + -2y3 = 0 Solving 30y + 42y2 + -2y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(15 + 21y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(15 + 21y + -1y2)' equal to zero and attempt to solve: Simplifying 15 + 21y + -1y2 = 0 Solving 15 + 21y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -21y + y2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -21y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + -21y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -21y + y2 = 0 + 15 -21y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 -21y + y2 = 15 The y term is -21y. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21y + 110.25 + y2 = 15 + 110.25 Reorder the terms: 110.25 + -21y + y2 = 15 + 110.25 Combine like terms: 15 + 110.25 = 125.25 110.25 + -21y + y2 = 125.25 Factor a perfect square on the left side: (y + -10.5)(y + -10.5) = 125.25 Calculate the square root of the right side: 11.191514643 Break this problem into two subproblems by setting (y + -10.5) equal to 11.191514643 and -11.191514643.Subproblem 1
y + -10.5 = 11.191514643 Simplifying y + -10.5 = 11.191514643 Reorder the terms: -10.5 + y = 11.191514643 Solving -10.5 + y = 11.191514643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = 11.191514643 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = 11.191514643 + 10.5 y = 11.191514643 + 10.5 Combine like terms: 11.191514643 + 10.5 = 21.691514643 y = 21.691514643 Simplifying y = 21.691514643Subproblem 2
y + -10.5 = -11.191514643 Simplifying y + -10.5 = -11.191514643 Reorder the terms: -10.5 + y = -11.191514643 Solving -10.5 + y = -11.191514643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + y = -11.191514643 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + y = -11.191514643 + 10.5 y = -11.191514643 + 10.5 Combine like terms: -11.191514643 + 10.5 = -0.691514643 y = -0.691514643 Simplifying y = -0.691514643Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.691514643, -0.691514643}Solution
y = {0, 21.691514643, -0.691514643}
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