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Simplifying (7x2) + -43x + -310 = 0 Reorder the terms: -310 + -43x + (7x2) = 0 Solving -310 + -43x + (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'. -44.28571429 + -6.142857143x + x2 = 0 Move the constant term to the right: Add '44.28571429' to each side of the equation. -44.28571429 + -6.142857143x + 44.28571429 + x2 = 0 + 44.28571429 Reorder the terms: -44.28571429 + 44.28571429 + -6.142857143x + x2 = 0 + 44.28571429 Combine like terms: -44.28571429 + 44.28571429 = 0.00000000 0.00000000 + -6.142857143x + x2 = 0 + 44.28571429 -6.142857143x + x2 = 0 + 44.28571429 Combine like terms: 0 + 44.28571429 = 44.28571429 -6.142857143x + x2 = 44.28571429 The x term is -6.142857143x. Take half its coefficient (-3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. -6.142857143x + 9.433673473 + x2 = 44.28571429 + 9.433673473 Reorder the terms: 9.433673473 + -6.142857143x + x2 = 44.28571429 + 9.433673473 Combine like terms: 44.28571429 + 9.433673473 = 53.719387763 9.433673473 + -6.142857143x + x2 = 53.719387763 Factor a perfect square on the left side: ((x) + -3.071428572)((x) + -3.071428572) = 53.719387763 Calculate the square root of the right side: 7.329351115 Break this problem into two subproblems by setting ((x) + -3.071428572) equal to 7.329351115 and -7.329351115.Subproblem 1
(x) + -3.071428572 = 7.329351115 Simplifying (x) + -3.071428572 = 7.329351115 x + -3.071428572 = 7.329351115 Reorder the terms: -3.071428572 + x = 7.329351115 Solving -3.071428572 + x = 7.329351115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = 7.329351115 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = 7.329351115 + 3.071428572 x = 7.329351115 + 3.071428572 Combine like terms: 7.329351115 + 3.071428572 = 10.400779687 x = 10.400779687 Simplifying x = 10.400779687Subproblem 2
(x) + -3.071428572 = -7.329351115 Simplifying (x) + -3.071428572 = -7.329351115 x + -3.071428572 = -7.329351115 Reorder the terms: -3.071428572 + x = -7.329351115 Solving -3.071428572 + x = -7.329351115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = -7.329351115 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = -7.329351115 + 3.071428572 x = -7.329351115 + 3.071428572 Combine like terms: -7.329351115 + 3.071428572 = -4.257922543 x = -4.257922543 Simplifying x = -4.257922543Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.400779687, -4.257922543}
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