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Simplifying 5x(x + 3) = 0.333333333(9x + 18) + -5 Reorder the terms: 5x(3 + x) = 0.333333333(9x + 18) + -5 (3 * 5x + x * 5x) = 0.333333333(9x + 18) + -5 (15x + 5x2) = 0.333333333(9x + 18) + -5 Reorder the terms: 15x + 5x2 = 0.333333333(18 + 9x) + -5 15x + 5x2 = (18 * 0.333333333 + 9x * 0.333333333) + -5 15x + 5x2 = (5.999999994 + 2.999999997x) + -5 Reorder the terms: 15x + 5x2 = 5.999999994 + -5 + 2.999999997x Combine like terms: 5.999999994 + -5 = 0.999999994 15x + 5x2 = 0.999999994 + 2.999999997x Solving 15x + 5x2 = 0.999999994 + 2.999999997x Solving for variable 'x'. Reorder the terms: -0.999999994 + 15x + -2.999999997x + 5x2 = 0.999999994 + 2.999999997x + -0.999999994 + -2.999999997x Combine like terms: 15x + -2.999999997x = 12.000000003x -0.999999994 + 12.000000003x + 5x2 = 0.999999994 + 2.999999997x + -0.999999994 + -2.999999997x Reorder the terms: -0.999999994 + 12.000000003x + 5x2 = 0.999999994 + -0.999999994 + 2.999999997x + -2.999999997x Combine like terms: 0.999999994 + -0.999999994 = 0.000000000 -0.999999994 + 12.000000003x + 5x2 = 0.000000000 + 2.999999997x + -2.999999997x -0.999999994 + 12.000000003x + 5x2 = 2.999999997x + -2.999999997x Combine like terms: 2.999999997x + -2.999999997x = 0.000000000 -0.999999994 + 12.000000003x + 5x2 = 0.000000000 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.1999999988 + 2.400000001x + x2 = 0.000000000 Move the constant term to the right: Add '0.1999999988' to each side of the equation. -0.1999999988 + 2.400000001x + 0.1999999988 + x2 = 0.000000000 + 0.1999999988 Reorder the terms: -0.1999999988 + 0.1999999988 + 2.400000001x + x2 = 0.000000000 + 0.1999999988 Combine like terms: -0.1999999988 + 0.1999999988 = 0.0000000000 0.0000000000 + 2.400000001x + x2 = 0.000000000 + 0.1999999988 2.400000001x + x2 = 0.000000000 + 0.1999999988 Combine like terms: 0.000000000 + 0.1999999988 = 0.1999999988 2.400000001x + x2 = 0.1999999988 The x term is 2.400000001x. Take half its coefficient (1.200000001). Square it (1.440000002) and add it to both sides. Add '1.440000002' to each side of the equation. 2.400000001x + 1.440000002 + x2 = 0.1999999988 + 1.440000002 Reorder the terms: 1.440000002 + 2.400000001x + x2 = 0.1999999988 + 1.440000002 Combine like terms: 0.1999999988 + 1.440000002 = 1.6400000008 1.440000002 + 2.400000001x + x2 = 1.6400000008 Factor a perfect square on the left side: (x + 1.200000001)(x + 1.200000001) = 1.6400000008 Calculate the square root of the right side: 1.280624848 Break this problem into two subproblems by setting (x + 1.200000001) equal to 1.280624848 and -1.280624848.Subproblem 1
x + 1.200000001 = 1.280624848 Simplifying x + 1.200000001 = 1.280624848 Reorder the terms: 1.200000001 + x = 1.280624848 Solving 1.200000001 + x = 1.280624848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.200000001' to each side of the equation. 1.200000001 + -1.200000001 + x = 1.280624848 + -1.200000001 Combine like terms: 1.200000001 + -1.200000001 = 0.000000000 0.000000000 + x = 1.280624848 + -1.200000001 x = 1.280624848 + -1.200000001 Combine like terms: 1.280624848 + -1.200000001 = 0.080624847 x = 0.080624847 Simplifying x = 0.080624847Subproblem 2
x + 1.200000001 = -1.280624848 Simplifying x + 1.200000001 = -1.280624848 Reorder the terms: 1.200000001 + x = -1.280624848 Solving 1.200000001 + x = -1.280624848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.200000001' to each side of the equation. 1.200000001 + -1.200000001 + x = -1.280624848 + -1.200000001 Combine like terms: 1.200000001 + -1.200000001 = 0.000000000 0.000000000 + x = -1.280624848 + -1.200000001 x = -1.280624848 + -1.200000001 Combine like terms: -1.280624848 + -1.200000001 = -2.480624849 x = -2.480624849 Simplifying x = -2.480624849Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.080624847, -2.480624849}
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