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Simplifying 3.8x2 + 1.2x + 17 = 1000 Reorder the terms: 17 + 1.2x + 3.8x2 = 1000 Solving 17 + 1.2x + 3.8x2 = 1000 Solving for variable 'x'. Reorder the terms: 17 + -1000 + 1.2x + 3.8x2 = 1000 + -1000 Combine like terms: 17 + -1000 = -983 -983 + 1.2x + 3.8x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -983 + 1.2x + 3.8x2 = 0 Begin completing the square. Divide all terms by 3.8 the coefficient of the squared term: Divide each side by '3.8'. -258.6842105 + 0.3157894737x + x2 = 0 Move the constant term to the right: Add '258.6842105' to each side of the equation. -258.6842105 + 0.3157894737x + 258.6842105 + x2 = 0 + 258.6842105 Reorder the terms: -258.6842105 + 258.6842105 + 0.3157894737x + x2 = 0 + 258.6842105 Combine like terms: -258.6842105 + 258.6842105 = 0.0000000 0.0000000 + 0.3157894737x + x2 = 0 + 258.6842105 0.3157894737x + x2 = 0 + 258.6842105 Combine like terms: 0 + 258.6842105 = 258.6842105 0.3157894737x + x2 = 258.6842105 The x term is 0.3157894737x. Take half its coefficient (0.1578947369). Square it (0.02493074794) and add it to both sides. Add '0.02493074794' to each side of the equation. 0.3157894737x + 0.02493074794 + x2 = 258.6842105 + 0.02493074794 Reorder the terms: 0.02493074794 + 0.3157894737x + x2 = 258.6842105 + 0.02493074794 Combine like terms: 258.6842105 + 0.02493074794 = 258.70914124794 0.02493074794 + 0.3157894737x + x2 = 258.70914124794 Factor a perfect square on the left side: (x + 0.1578947369)(x + 0.1578947369) = 258.70914124794 Calculate the square root of the right side: 16.084437859 Break this problem into two subproblems by setting (x + 0.1578947369) equal to 16.084437859 and -16.084437859.Subproblem 1
x + 0.1578947369 = 16.084437859 Simplifying x + 0.1578947369 = 16.084437859 Reorder the terms: 0.1578947369 + x = 16.084437859 Solving 0.1578947369 + x = 16.084437859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1578947369' to each side of the equation. 0.1578947369 + -0.1578947369 + x = 16.084437859 + -0.1578947369 Combine like terms: 0.1578947369 + -0.1578947369 = 0.0000000000 0.0000000000 + x = 16.084437859 + -0.1578947369 x = 16.084437859 + -0.1578947369 Combine like terms: 16.084437859 + -0.1578947369 = 15.9265431221 x = 15.9265431221 Simplifying x = 15.9265431221Subproblem 2
x + 0.1578947369 = -16.084437859 Simplifying x + 0.1578947369 = -16.084437859 Reorder the terms: 0.1578947369 + x = -16.084437859 Solving 0.1578947369 + x = -16.084437859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1578947369' to each side of the equation. 0.1578947369 + -0.1578947369 + x = -16.084437859 + -0.1578947369 Combine like terms: 0.1578947369 + -0.1578947369 = 0.0000000000 0.0000000000 + x = -16.084437859 + -0.1578947369 x = -16.084437859 + -0.1578947369 Combine like terms: -16.084437859 + -0.1578947369 = -16.2423325959 x = -16.2423325959 Simplifying x = -16.2423325959Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.9265431221, -16.2423325959}
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