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Simplifying 1700 + -253x + -7x2 = 0 Solving 1700 + -253x + -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'. -242.8571429 + 36.14285714x + x2 = 0 Move the constant term to the right: Add '242.8571429' to each side of the equation. -242.8571429 + 36.14285714x + 242.8571429 + x2 = 0 + 242.8571429 Reorder the terms: -242.8571429 + 242.8571429 + 36.14285714x + x2 = 0 + 242.8571429 Combine like terms: -242.8571429 + 242.8571429 = 0.0000000 0.0000000 + 36.14285714x + x2 = 0 + 242.8571429 36.14285714x + x2 = 0 + 242.8571429 Combine like terms: 0 + 242.8571429 = 242.8571429 36.14285714x + x2 = 242.8571429 The x term is 36.14285714x. Take half its coefficient (18.07142857). Square it (326.5765306) and add it to both sides. Add '326.5765306' to each side of the equation. 36.14285714x + 326.5765306 + x2 = 242.8571429 + 326.5765306 Reorder the terms: 326.5765306 + 36.14285714x + x2 = 242.8571429 + 326.5765306 Combine like terms: 242.8571429 + 326.5765306 = 569.4336735 326.5765306 + 36.14285714x + x2 = 569.4336735 Factor a perfect square on the left side: (x + 18.07142857)(x + 18.07142857) = 569.4336735 Calculate the square root of the right side: 23.862809422 Break this problem into two subproblems by setting (x + 18.07142857) equal to 23.862809422 and -23.862809422.Subproblem 1
x + 18.07142857 = 23.862809422 Simplifying x + 18.07142857 = 23.862809422 Reorder the terms: 18.07142857 + x = 23.862809422 Solving 18.07142857 + x = 23.862809422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.07142857' to each side of the equation. 18.07142857 + -18.07142857 + x = 23.862809422 + -18.07142857 Combine like terms: 18.07142857 + -18.07142857 = 0.00000000 0.00000000 + x = 23.862809422 + -18.07142857 x = 23.862809422 + -18.07142857 Combine like terms: 23.862809422 + -18.07142857 = 5.791380852 x = 5.791380852 Simplifying x = 5.791380852Subproblem 2
x + 18.07142857 = -23.862809422 Simplifying x + 18.07142857 = -23.862809422 Reorder the terms: 18.07142857 + x = -23.862809422 Solving 18.07142857 + x = -23.862809422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.07142857' to each side of the equation. 18.07142857 + -18.07142857 + x = -23.862809422 + -18.07142857 Combine like terms: 18.07142857 + -18.07142857 = 0.00000000 0.00000000 + x = -23.862809422 + -18.07142857 x = -23.862809422 + -18.07142857 Combine like terms: -23.862809422 + -18.07142857 = -41.934237992 x = -41.934237992 Simplifying x = -41.934237992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.791380852, -41.934237992}
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