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Simplifying 7x2 + 3x + -2000 = 0 Reorder the terms: -2000 + 3x + 7x2 = 0 Solving -2000 + 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'. -285.7142857 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '285.7142857' to each side of the equation. -285.7142857 + 0.4285714286x + 285.7142857 + x2 = 0 + 285.7142857 Reorder the terms: -285.7142857 + 285.7142857 + 0.4285714286x + x2 = 0 + 285.7142857 Combine like terms: -285.7142857 + 285.7142857 = 0.0000000 0.0000000 + 0.4285714286x + x2 = 0 + 285.7142857 0.4285714286x + x2 = 0 + 285.7142857 Combine like terms: 0 + 285.7142857 = 285.7142857 0.4285714286x + x2 = 285.7142857 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 = 285.7142857 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 285.7142857 + 0.04591836735 Combine like terms: 285.7142857 + 0.04591836735 = 285.76020406735 0.04591836735 + 0.4285714286x + x2 = 285.76020406735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 285.76020406735 Calculate the square root of the right side: 16.904443323 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 16.904443323 and -16.904443323.Subproblem 1
x + 0.2142857143 = 16.904443323 Simplifying x + 0.2142857143 = 16.904443323 Reorder the terms: 0.2142857143 + x = 16.904443323 Solving 0.2142857143 + x = 16.904443323 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 = 16.904443323 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 16.904443323 + -0.2142857143 x = 16.904443323 + -0.2142857143 Combine like terms: 16.904443323 + -0.2142857143 = 16.6901576087 x = 16.6901576087 Simplifying x = 16.6901576087Subproblem 2
x + 0.2142857143 = -16.904443323 Simplifying x + 0.2142857143 = -16.904443323 Reorder the terms: 0.2142857143 + x = -16.904443323 Solving 0.2142857143 + x = -16.904443323 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 = -16.904443323 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -16.904443323 + -0.2142857143 x = -16.904443323 + -0.2142857143 Combine like terms: -16.904443323 + -0.2142857143 = -17.1187290373 x = -17.1187290373 Simplifying x = -17.1187290373Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.6901576087, -17.1187290373}
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