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Simplifying 7x2 + -260x + 1000 = 0 Reorder the terms: 1000 + -260x + 7x2 = 0 Solving 1000 + -260x + 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'. 142.8571429 + -37.14285714x + x2 = 0 Move the constant term to the right: Add '-142.8571429' to each side of the equation. 142.8571429 + -37.14285714x + -142.8571429 + x2 = 0 + -142.8571429 Reorder the terms: 142.8571429 + -142.8571429 + -37.14285714x + x2 = 0 + -142.8571429 Combine like terms: 142.8571429 + -142.8571429 = 0.0000000 0.0000000 + -37.14285714x + x2 = 0 + -142.8571429 -37.14285714x + x2 = 0 + -142.8571429 Combine like terms: 0 + -142.8571429 = -142.8571429 -37.14285714x + x2 = -142.8571429 The x term is -37.14285714x. Take half its coefficient (-18.57142857). Square it (344.8979591) and add it to both sides. Add '344.8979591' to each side of the equation. -37.14285714x + 344.8979591 + x2 = -142.8571429 + 344.8979591 Reorder the terms: 344.8979591 + -37.14285714x + x2 = -142.8571429 + 344.8979591 Combine like terms: -142.8571429 + 344.8979591 = 202.0408162 344.8979591 + -37.14285714x + x2 = 202.0408162 Factor a perfect square on the left side: (x + -18.57142857)(x + -18.57142857) = 202.0408162 Calculate the square root of the right side: 14.21410624 Break this problem into two subproblems by setting (x + -18.57142857) equal to 14.21410624 and -14.21410624.Subproblem 1
x + -18.57142857 = 14.21410624 Simplifying x + -18.57142857 = 14.21410624 Reorder the terms: -18.57142857 + x = 14.21410624 Solving -18.57142857 + x = 14.21410624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.57142857' to each side of the equation. -18.57142857 + 18.57142857 + x = 14.21410624 + 18.57142857 Combine like terms: -18.57142857 + 18.57142857 = 0.00000000 0.00000000 + x = 14.21410624 + 18.57142857 x = 14.21410624 + 18.57142857 Combine like terms: 14.21410624 + 18.57142857 = 32.78553481 x = 32.78553481 Simplifying x = 32.78553481Subproblem 2
x + -18.57142857 = -14.21410624 Simplifying x + -18.57142857 = -14.21410624 Reorder the terms: -18.57142857 + x = -14.21410624 Solving -18.57142857 + x = -14.21410624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.57142857' to each side of the equation. -18.57142857 + 18.57142857 + x = -14.21410624 + 18.57142857 Combine like terms: -18.57142857 + 18.57142857 = 0.00000000 0.00000000 + x = -14.21410624 + 18.57142857 x = -14.21410624 + 18.57142857 Combine like terms: -14.21410624 + 18.57142857 = 4.35732233 x = 4.35732233 Simplifying x = 4.35732233Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.78553481, 4.35732233}
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