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Simplifying 7x2 + 3x + -6000 = 0 Reorder the terms: -6000 + 3x + 7x2 = 0 Solving -6000 + 3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -857.1428571 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '857.1428571' to each side of the equation. -857.1428571 + 0.4285714286x + 857.1428571 + x2 = 0 + 857.1428571 Reorder the terms: -857.1428571 + 857.1428571 + 0.4285714286x + x2 = 0 + 857.1428571 Combine like terms: -857.1428571 + 857.1428571 = 0.0000000 0.0000000 + 0.4285714286x + x2 = 0 + 857.1428571 0.4285714286x + x2 = 0 + 857.1428571 Combine like terms: 0 + 857.1428571 = 857.1428571 0.4285714286x + x2 = 857.1428571 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 857.1428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 857.1428571 + 0.04591836735 Combine like terms: 857.1428571 + 0.04591836735 = 857.18877546735 0.04591836735 + 0.4285714286x + x2 = 857.18877546735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 857.18877546735 Calculate the square root of the right side: 29.277786383 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 29.277786383 and -29.277786383.Subproblem 1
x + 0.2142857143 = 29.277786383 Simplifying x + 0.2142857143 = 29.277786383 Reorder the terms: 0.2142857143 + x = 29.277786383 Solving 0.2142857143 + x = 29.277786383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 29.277786383 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 29.277786383 + -0.2142857143 x = 29.277786383 + -0.2142857143 Combine like terms: 29.277786383 + -0.2142857143 = 29.0635006687 x = 29.0635006687 Simplifying x = 29.0635006687Subproblem 2
x + 0.2142857143 = -29.277786383 Simplifying x + 0.2142857143 = -29.277786383 Reorder the terms: 0.2142857143 + x = -29.277786383 Solving 0.2142857143 + x = -29.277786383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -29.277786383 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -29.277786383 + -0.2142857143 x = -29.277786383 + -0.2142857143 Combine like terms: -29.277786383 + -0.2142857143 = -29.4920720973 x = -29.4920720973 Simplifying x = -29.4920720973Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.0635006687, -29.4920720973}
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