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Simplifying 3a2 + 3a + -20 = 0 Reorder the terms: -20 + 3a + 3a2 = 0 Solving -20 + 3a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + a + a2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + a + 6.666666667 + a2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + a + a2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + a + a2 = 0 + 6.666666667 a + a2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 a + a2 = 6.666666667 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 6.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 6.666666667 + 0.25 Combine like terms: 6.666666667 + 0.25 = 6.916666667 1.25 + a2 = 6.916666667 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 6.916666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (a + 0.5) equal to 2.62995564 and -2.62995564.Subproblem 1
a + 0.5 = 2.62995564 Simplifying a + 0.5 = 2.62995564 Reorder the terms: 0.5 + a = 2.62995564 Solving 0.5 + a = 2.62995564 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 2.62995564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2.62995564 + -0.5 a = 2.62995564 + -0.5 Combine like terms: 2.62995564 + -0.5 = 2.12995564 a = 2.12995564 Simplifying a = 2.12995564Subproblem 2
a + 0.5 = -2.62995564 Simplifying a + 0.5 = -2.62995564 Reorder the terms: 0.5 + a = -2.62995564 Solving 0.5 + a = -2.62995564 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -2.62995564 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2.62995564 + -0.5 a = -2.62995564 + -0.5 Combine like terms: -2.62995564 + -0.5 = -3.12995564 a = -3.12995564 Simplifying a = -3.12995564Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.12995564, -3.12995564}
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