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Simplifying 7x2 = 2 + -11x Solving 7x2 = 2 + -11x Solving for variable 'x'. Reorder the terms: -2 + 11x + 7x2 = 2 + -11x + -2 + 11x Reorder the terms: -2 + 11x + 7x2 = 2 + -2 + -11x + 11x Combine like terms: 2 + -2 = 0 -2 + 11x + 7x2 = 0 + -11x + 11x -2 + 11x + 7x2 = -11x + 11x Combine like terms: -11x + 11x = 0 -2 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 1.571428571x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 1.571428571x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 1.571428571x + x2 = 0 + 0.2857142857 1.571428571x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 1.571428571x + x2 = 0.2857142857 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = 0.2857142857 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = 0.2857142857 + 0.6173469384 Combine like terms: 0.2857142857 + 0.6173469384 = 0.9030612241 0.6173469384 + 1.571428571x + x2 = 0.9030612241 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 0.9030612241 Calculate the square root of the right side: 0.950295335 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 0.950295335 and -0.950295335.Subproblem 1
x + 0.7857142855 = 0.950295335 Simplifying x + 0.7857142855 = 0.950295335 Reorder the terms: 0.7857142855 + x = 0.950295335 Solving 0.7857142855 + x = 0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 0.950295335 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 0.950295335 + -0.7857142855 x = 0.950295335 + -0.7857142855 Combine like terms: 0.950295335 + -0.7857142855 = 0.1645810495 x = 0.1645810495 Simplifying x = 0.1645810495Subproblem 2
x + 0.7857142855 = -0.950295335 Simplifying x + 0.7857142855 = -0.950295335 Reorder the terms: 0.7857142855 + x = -0.950295335 Solving 0.7857142855 + x = -0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -0.950295335 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -0.950295335 + -0.7857142855 x = -0.950295335 + -0.7857142855 Combine like terms: -0.950295335 + -0.7857142855 = -1.7360096205 x = -1.7360096205 Simplifying x = -1.7360096205Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1645810495, -1.7360096205}
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