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Simplifying 0 = 0.0003x2 + 4.2x + 1000 Reorder the terms: 0 = 1000 + 4.2x + 0.0003x2 Solving 0 = 1000 + 4.2x + 0.0003x2 Solving for variable 'x'. Combine like terms: 0 + -1000 = -1000 -1000 + -4.2x + -0.0003x2 = 1000 + 4.2x + 0.0003x2 + -1000 + -4.2x + -0.0003x2 Reorder the terms: -1000 + -4.2x + -0.0003x2 = 1000 + -1000 + 4.2x + -4.2x + 0.0003x2 + -0.0003x2 Combine like terms: 1000 + -1000 = 0 -1000 + -4.2x + -0.0003x2 = 0 + 4.2x + -4.2x + 0.0003x2 + -0.0003x2 -1000 + -4.2x + -0.0003x2 = 4.2x + -4.2x + 0.0003x2 + -0.0003x2 Combine like terms: 4.2x + -4.2x = 0.0 -1000 + -4.2x + -0.0003x2 = 0.0 + 0.0003x2 + -0.0003x2 -1000 + -4.2x + -0.0003x2 = 0.0003x2 + -0.0003x2 Combine like terms: 0.0003x2 + -0.0003x2 = 0.0000 -1000 + -4.2x + -0.0003x2 = 0.0000 Begin completing the square. Divide all terms by -0.0003 the coefficient of the squared term: Divide each side by '-0.0003'. 3333333.333 + 14000x + x2 = 0 Move the constant term to the right: Add '-3333333.333' to each side of the equation. 3333333.333 + 14000x + -3333333.333 + x2 = 0 + -3333333.333 Reorder the terms: 3333333.333 + -3333333.333 + 14000x + x2 = 0 + -3333333.333 Combine like terms: 3333333.333 + -3333333.333 = 0.000 0.000 + 14000x + x2 = 0 + -3333333.333 14000x + x2 = 0 + -3333333.333 Combine like terms: 0 + -3333333.333 = -3333333.333 14000x + x2 = -3333333.333 The x term is 14000x. Take half its coefficient (7000). Square it (49000000) and add it to both sides. Add '49000000' to each side of the equation. 14000x + 49000000 + x2 = -3333333.333 + 49000000 Reorder the terms: 49000000 + 14000x + x2 = -3333333.333 + 49000000 Combine like terms: -3333333.333 + 49000000 = 45666666.667 49000000 + 14000x + x2 = 45666666.667 Factor a perfect square on the left side: (x + 7000)(x + 7000) = 45666666.667 Calculate the square root of the right side: 6757.711644262 Break this problem into two subproblems by setting (x + 7000) equal to 6757.711644262 and -6757.711644262.Subproblem 1
x + 7000 = 6757.711644262 Simplifying x + 7000 = 6757.711644262 Reorder the terms: 7000 + x = 6757.711644262 Solving 7000 + x = 6757.711644262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7000' to each side of the equation. 7000 + -7000 + x = 6757.711644262 + -7000 Combine like terms: 7000 + -7000 = 0 0 + x = 6757.711644262 + -7000 x = 6757.711644262 + -7000 Combine like terms: 6757.711644262 + -7000 = -242.288355738 x = -242.288355738 Simplifying x = -242.288355738Subproblem 2
x + 7000 = -6757.711644262 Simplifying x + 7000 = -6757.711644262 Reorder the terms: 7000 + x = -6757.711644262 Solving 7000 + x = -6757.711644262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7000' to each side of the equation. 7000 + -7000 + x = -6757.711644262 + -7000 Combine like terms: 7000 + -7000 = 0 0 + x = -6757.711644262 + -7000 x = -6757.711644262 + -7000 Combine like terms: -6757.711644262 + -7000 = -13757.711644262 x = -13757.711644262 Simplifying x = -13757.711644262Solution
The solution to the problem is based on the solutions from the subproblems. x = {-242.288355738, -13757.711644262}
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