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Simplifying 15y3 + -24y2 + -64y = 0 Reorder the terms: -64y + -24y2 + 15y3 = 0 Solving -64y + -24y2 + 15y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-64 + -24y + 15y2) = 0Subproblem 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 '(-64 + -24y + 15y2)' equal to zero and attempt to solve: Simplifying -64 + -24y + 15y2 = 0 Solving -64 + -24y + 15y2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.266666667 + -1.6y + y2 = 0 Move the constant term to the right: Add '4.266666667' to each side of the equation. -4.266666667 + -1.6y + 4.266666667 + y2 = 0 + 4.266666667 Reorder the terms: -4.266666667 + 4.266666667 + -1.6y + y2 = 0 + 4.266666667 Combine like terms: -4.266666667 + 4.266666667 = 0.000000000 0.000000000 + -1.6y + y2 = 0 + 4.266666667 -1.6y + y2 = 0 + 4.266666667 Combine like terms: 0 + 4.266666667 = 4.266666667 -1.6y + y2 = 4.266666667 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = 4.266666667 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 4.266666667 + 0.64 Combine like terms: 4.266666667 + 0.64 = 4.906666667 0.64 + -1.6y + y2 = 4.906666667 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 4.906666667 Calculate the square root of the right side: 2.215099697 Break this problem into two subproblems by setting (y + -0.8) equal to 2.215099697 and -2.215099697.Subproblem 1
y + -0.8 = 2.215099697 Simplifying y + -0.8 = 2.215099697 Reorder the terms: -0.8 + y = 2.215099697 Solving -0.8 + y = 2.215099697 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = 2.215099697 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 2.215099697 + 0.8 y = 2.215099697 + 0.8 Combine like terms: 2.215099697 + 0.8 = 3.015099697 y = 3.015099697 Simplifying y = 3.015099697Subproblem 2
y + -0.8 = -2.215099697 Simplifying y + -0.8 = -2.215099697 Reorder the terms: -0.8 + y = -2.215099697 Solving -0.8 + y = -2.215099697 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = -2.215099697 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -2.215099697 + 0.8 y = -2.215099697 + 0.8 Combine like terms: -2.215099697 + 0.8 = -1.415099697 y = -1.415099697 Simplifying y = -1.415099697Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.015099697, -1.415099697}Solution
y = {0, 3.015099697, -1.415099697}
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