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Simplifying 295840000 = x(x + 4000) Reorder the terms: 295840000 = x(4000 + x) 295840000 = (4000 * x + x * x) 295840000 = (4000x + x2) Solving 295840000 = 4000x + x2 Solving for variable 'x'. Reorder the terms: 295840000 + -4000x + -1x2 = 4000x + -4000x + x2 + -1x2 Combine like terms: 4000x + -4000x = 0 295840000 + -4000x + -1x2 = 0 + x2 + -1x2 295840000 + -4000x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 295840000 + -4000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -295840000 + 4000x + x2 = 0 Move the constant term to the right: Add '295840000' to each side of the equation. -295840000 + 4000x + 295840000 + x2 = 0 + 295840000 Reorder the terms: -295840000 + 295840000 + 4000x + x2 = 0 + 295840000 Combine like terms: -295840000 + 295840000 = 0 0 + 4000x + x2 = 0 + 295840000 4000x + x2 = 0 + 295840000 Combine like terms: 0 + 295840000 = 295840000 4000x + x2 = 295840000 The x term is 4000x. Take half its coefficient (2000). Square it (4000000) and add it to both sides. Add '4000000' to each side of the equation. 4000x + 4000000 + x2 = 295840000 + 4000000 Reorder the terms: 4000000 + 4000x + x2 = 295840000 + 4000000 Combine like terms: 295840000 + 4000000 = 299840000 4000000 + 4000x + x2 = 299840000 Factor a perfect square on the left side: (x + 2000)(x + 2000) = 299840000 Calculate the square root of the right side: 17315.888657531 Break this problem into two subproblems by setting (x + 2000) equal to 17315.888657531 and -17315.888657531.Subproblem 1
x + 2000 = 17315.888657531 Simplifying x + 2000 = 17315.888657531 Reorder the terms: 2000 + x = 17315.888657531 Solving 2000 + x = 17315.888657531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = 17315.888657531 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = 17315.888657531 + -2000 x = 17315.888657531 + -2000 Combine like terms: 17315.888657531 + -2000 = 15315.888657531 x = 15315.888657531 Simplifying x = 15315.888657531Subproblem 2
x + 2000 = -17315.888657531 Simplifying x + 2000 = -17315.888657531 Reorder the terms: 2000 + x = -17315.888657531 Solving 2000 + x = -17315.888657531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = -17315.888657531 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = -17315.888657531 + -2000 x = -17315.888657531 + -2000 Combine like terms: -17315.888657531 + -2000 = -19315.888657531 x = -19315.888657531 Simplifying x = -19315.888657531Solution
The solution to the problem is based on the solutions from the subproblems. x = {15315.888657531, -19315.888657531}
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