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Simplifying 14y2 + 6y + -30 = 0 Reorder the terms: -30 + 6y + 14y2 = 0 Solving -30 + 6y + 14y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 3y + 7y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 3y + 7y2)' equal to zero and attempt to solve: Simplifying -15 + 3y + 7y2 = 0 Solving -15 + 3y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + 0.4285714286y + y2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 0.4285714286y + 2.142857143 + y2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 0.4285714286y + y2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 0.4285714286y + y2 = 0 + 2.142857143 0.4285714286y + y2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 0.4285714286y + y2 = 2.142857143 The y term is 0.4285714286y. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286y + 0.04591836735 + y2 = 2.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286y + y2 = 2.142857143 + 0.04591836735 Combine like terms: 2.142857143 + 0.04591836735 = 2.18877551035 0.04591836735 + 0.4285714286y + y2 = 2.18877551035 Factor a perfect square on the left side: (y + 0.2142857143)(y + 0.2142857143) = 2.18877551035 Calculate the square root of the right side: 1.479451084 Break this problem into two subproblems by setting (y + 0.2142857143) equal to 1.479451084 and -1.479451084.Subproblem 1
y + 0.2142857143 = 1.479451084 Simplifying y + 0.2142857143 = 1.479451084 Reorder the terms: 0.2142857143 + y = 1.479451084 Solving 0.2142857143 + y = 1.479451084 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + y = 1.479451084 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + y = 1.479451084 + -0.2142857143 y = 1.479451084 + -0.2142857143 Combine like terms: 1.479451084 + -0.2142857143 = 1.2651653697 y = 1.2651653697 Simplifying y = 1.2651653697Subproblem 2
y + 0.2142857143 = -1.479451084 Simplifying y + 0.2142857143 = -1.479451084 Reorder the terms: 0.2142857143 + y = -1.479451084 Solving 0.2142857143 + y = -1.479451084 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + y = -1.479451084 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + y = -1.479451084 + -0.2142857143 y = -1.479451084 + -0.2142857143 Combine like terms: -1.479451084 + -0.2142857143 = -1.6937367983 y = -1.6937367983 Simplifying y = -1.6937367983Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2651653697, -1.6937367983}Solution
y = {1.2651653697, -1.6937367983}
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