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Simplifying 7x2 + 73x + -154 = 0 Reorder the terms: -154 + 73x + 7x2 = 0 Solving -154 + 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'. -22 + 10.42857143x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 10.42857143x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 10.42857143x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 10.42857143x + x2 = 0 + 22 10.42857143x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 10.42857143x + x2 = 22 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 = 22 + 27.18877552 Reorder the terms: 27.18877552 + 10.42857143x + x2 = 22 + 27.18877552 Combine like terms: 22 + 27.18877552 = 49.18877552 27.18877552 + 10.42857143x + x2 = 49.18877552 Factor a perfect square on the left side: (x + 5.214285715)(x + 5.214285715) = 49.18877552 Calculate the square root of the right side: 7.013471004 Break this problem into two subproblems by setting (x + 5.214285715) equal to 7.013471004 and -7.013471004.Subproblem 1
x + 5.214285715 = 7.013471004 Simplifying x + 5.214285715 = 7.013471004 Reorder the terms: 5.214285715 + x = 7.013471004 Solving 5.214285715 + x = 7.013471004 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 = 7.013471004 + -5.214285715 Combine like terms: 5.214285715 + -5.214285715 = 0.000000000 0.000000000 + x = 7.013471004 + -5.214285715 x = 7.013471004 + -5.214285715 Combine like terms: 7.013471004 + -5.214285715 = 1.799185289 x = 1.799185289 Simplifying x = 1.799185289Subproblem 2
x + 5.214285715 = -7.013471004 Simplifying x + 5.214285715 = -7.013471004 Reorder the terms: 5.214285715 + x = -7.013471004 Solving 5.214285715 + x = -7.013471004 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 = -7.013471004 + -5.214285715 Combine like terms: 5.214285715 + -5.214285715 = 0.000000000 0.000000000 + x = -7.013471004 + -5.214285715 x = -7.013471004 + -5.214285715 Combine like terms: -7.013471004 + -5.214285715 = -12.227756719 x = -12.227756719 Simplifying x = -12.227756719Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.799185289, -12.227756719}
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