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Simplifying (3x)(3x + 1) = 98 Remove parenthesis around (3x) 3x(3x + 1) = 98 Reorder the terms: 3x(1 + 3x) = 98 (1 * 3x + 3x * 3x) = 98 (3x + 9x2) = 98 Solving 3x + 9x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 3x + 9x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -10.88888889 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '10.88888889' to each side of the equation. -10.88888889 + 0.3333333333x + 10.88888889 + x2 = 0 + 10.88888889 Reorder the terms: -10.88888889 + 10.88888889 + 0.3333333333x + x2 = 0 + 10.88888889 Combine like terms: -10.88888889 + 10.88888889 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 10.88888889 0.3333333333x + x2 = 0 + 10.88888889 Combine like terms: 0 + 10.88888889 = 10.88888889 0.3333333333x + x2 = 10.88888889 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 10.88888889 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 10.88888889 + 0.02777777779 Combine like terms: 10.88888889 + 0.02777777779 = 10.91666666779 0.02777777779 + 0.3333333333x + x2 = 10.91666666779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 10.91666666779 Calculate the square root of the right side: 3.304037934 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 3.304037934 and -3.304037934.Subproblem 1
x + 0.1666666667 = 3.304037934 Simplifying x + 0.1666666667 = 3.304037934 Reorder the terms: 0.1666666667 + x = 3.304037934 Solving 0.1666666667 + x = 3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 3.304037934 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 3.304037934 + -0.1666666667 x = 3.304037934 + -0.1666666667 Combine like terms: 3.304037934 + -0.1666666667 = 3.1373712673 x = 3.1373712673 Simplifying x = 3.1373712673Subproblem 2
x + 0.1666666667 = -3.304037934 Simplifying x + 0.1666666667 = -3.304037934 Reorder the terms: 0.1666666667 + x = -3.304037934 Solving 0.1666666667 + x = -3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -3.304037934 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -3.304037934 + -0.1666666667 x = -3.304037934 + -0.1666666667 Combine like terms: -3.304037934 + -0.1666666667 = -3.4707046007 x = -3.4707046007 Simplifying x = -3.4707046007Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1373712673, -3.4707046007}
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