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Simplifying (-2)(5y2 + 3y + -9) = 0 Reorder the terms: -2(-9 + 3y + 5y2) = 0 (-9 * -2 + 3y * -2 + 5y2 * -2) = 0 (18 + -6y + -10y2) = 0 Solving 18 + -6y + -10y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -3y + -5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -3y + -5y2)' equal to zero and attempt to solve: Simplifying 9 + -3y + -5y2 = 0 Solving 9 + -3y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + 0.6y + y2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.6y + 1.8 + y2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.6y + y2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.6y + y2 = 0 + 1.8 0.6y + y2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.6y + y2 = 1.8 The y term is 0.6y. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6y + 0.09 + y2 = 1.8 + 0.09 Reorder the terms: 0.09 + 0.6y + y2 = 1.8 + 0.09 Combine like terms: 1.8 + 0.09 = 1.89 0.09 + 0.6y + y2 = 1.89 Factor a perfect square on the left side: (y + 0.3)(y + 0.3) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (y + 0.3) equal to 1.374772708 and -1.374772708.Subproblem 1
y + 0.3 = 1.374772708 Simplifying y + 0.3 = 1.374772708 Reorder the terms: 0.3 + y = 1.374772708 Solving 0.3 + y = 1.374772708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = 1.374772708 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = 1.374772708 + -0.3 y = 1.374772708 + -0.3 Combine like terms: 1.374772708 + -0.3 = 1.074772708 y = 1.074772708 Simplifying y = 1.074772708Subproblem 2
y + 0.3 = -1.374772708 Simplifying y + 0.3 = -1.374772708 Reorder the terms: 0.3 + y = -1.374772708 Solving 0.3 + y = -1.374772708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = -1.374772708 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = -1.374772708 + -0.3 y = -1.374772708 + -0.3 Combine like terms: -1.374772708 + -0.3 = -1.674772708 y = -1.674772708 Simplifying y = -1.674772708Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.074772708, -1.674772708}Solution
y = {1.074772708, -1.674772708}
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