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Simplifying 3x2 + 10x + -216 = 0 Reorder the terms: -216 + 10x + 3x2 = 0 Solving -216 + 10x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -72 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 3.333333333x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 3.333333333x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 3.333333333x + x2 = 0 + 72 3.333333333x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 3.333333333x + x2 = 72 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 72 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 72 + 2.777777779 Combine like terms: 72 + 2.777777779 = 74.777777779 2.777777779 + 3.333333333x + x2 = 74.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 74.777777779 Calculate the square root of the right side: 8.647414514 Break this problem into two subproblems by setting (x + 1.666666667) equal to 8.647414514 and -8.647414514.Subproblem 1
x + 1.666666667 = 8.647414514 Simplifying x + 1.666666667 = 8.647414514 Reorder the terms: 1.666666667 + x = 8.647414514 Solving 1.666666667 + x = 8.647414514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 8.647414514 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 8.647414514 + -1.666666667 x = 8.647414514 + -1.666666667 Combine like terms: 8.647414514 + -1.666666667 = 6.980747847 x = 6.980747847 Simplifying x = 6.980747847Subproblem 2
x + 1.666666667 = -8.647414514 Simplifying x + 1.666666667 = -8.647414514 Reorder the terms: 1.666666667 + x = -8.647414514 Solving 1.666666667 + x = -8.647414514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -8.647414514 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -8.647414514 + -1.666666667 x = -8.647414514 + -1.666666667 Combine like terms: -8.647414514 + -1.666666667 = -10.314081181 x = -10.314081181 Simplifying x = -10.314081181Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.980747847, -10.314081181}
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