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Simplifying 7x2 + -73x + -137 = 0 Reorder the terms: -137 + -73x + 7x2 = 0 Solving -137 + -73x + 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'. -19.57142857 + -10.42857143x + x2 = 0 Move the constant term to the right: Add '19.57142857' to each side of the equation. -19.57142857 + -10.42857143x + 19.57142857 + x2 = 0 + 19.57142857 Reorder the terms: -19.57142857 + 19.57142857 + -10.42857143x + x2 = 0 + 19.57142857 Combine like terms: -19.57142857 + 19.57142857 = 0.00000000 0.00000000 + -10.42857143x + x2 = 0 + 19.57142857 -10.42857143x + x2 = 0 + 19.57142857 Combine like terms: 0 + 19.57142857 = 19.57142857 -10.42857143x + x2 = 19.57142857 The x term is -10.42857143x. Take half its coefficient (-5.214285715). Square it (27.18877552) and add it to both sides. Add '27.18877552' to each side of the equation. -10.42857143x + 27.18877552 + x2 = 19.57142857 + 27.18877552 Reorder the terms: 27.18877552 + -10.42857143x + x2 = 19.57142857 + 27.18877552 Combine like terms: 19.57142857 + 27.18877552 = 46.76020409 27.18877552 + -10.42857143x + x2 = 46.76020409 Factor a perfect square on the left side: (x + -5.214285715)(x + -5.214285715) = 46.76020409 Calculate the square root of the right side: 6.838143322 Break this problem into two subproblems by setting (x + -5.214285715) equal to 6.838143322 and -6.838143322.Subproblem 1
x + -5.214285715 = 6.838143322 Simplifying x + -5.214285715 = 6.838143322 Reorder the terms: -5.214285715 + x = 6.838143322 Solving -5.214285715 + x = 6.838143322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.214285715' to each side of the equation. -5.214285715 + 5.214285715 + x = 6.838143322 + 5.214285715 Combine like terms: -5.214285715 + 5.214285715 = 0.000000000 0.000000000 + x = 6.838143322 + 5.214285715 x = 6.838143322 + 5.214285715 Combine like terms: 6.838143322 + 5.214285715 = 12.052429037 x = 12.052429037 Simplifying x = 12.052429037Subproblem 2
x + -5.214285715 = -6.838143322 Simplifying x + -5.214285715 = -6.838143322 Reorder the terms: -5.214285715 + x = -6.838143322 Solving -5.214285715 + x = -6.838143322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.214285715' to each side of the equation. -5.214285715 + 5.214285715 + x = -6.838143322 + 5.214285715 Combine like terms: -5.214285715 + 5.214285715 = 0.000000000 0.000000000 + x = -6.838143322 + 5.214285715 x = -6.838143322 + 5.214285715 Combine like terms: -6.838143322 + 5.214285715 = -1.623857607 x = -1.623857607 Simplifying x = -1.623857607Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.052429037, -1.623857607}
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