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Simplifying 7x2 + -8x + -18 = 0 Reorder the terms: -18 + -8x + 7x2 = 0 Solving -18 + -8x + 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'. -2.571428571 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -1.142857143x + 2.571428571 + x2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -1.142857143x + x2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 2.571428571 -1.142857143x + x2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -1.142857143x + x2 = 2.571428571 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 2.571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 2.571428571 + 0.3265306123 Combine like terms: 2.571428571 + 0.3265306123 = 2.8979591833 0.3265306123 + -1.142857143x + x2 = 2.8979591833 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 2.8979591833 Calculate the square root of the right side: 1.702339327 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.702339327 and -1.702339327.Subproblem 1
x + -0.5714285715 = 1.702339327 Simplifying x + -0.5714285715 = 1.702339327 Reorder the terms: -0.5714285715 + x = 1.702339327 Solving -0.5714285715 + x = 1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 1.702339327 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.702339327 + 0.5714285715 x = 1.702339327 + 0.5714285715 Combine like terms: 1.702339327 + 0.5714285715 = 2.2737678985 x = 2.2737678985 Simplifying x = 2.2737678985Subproblem 2
x + -0.5714285715 = -1.702339327 Simplifying x + -0.5714285715 = -1.702339327 Reorder the terms: -0.5714285715 + x = -1.702339327 Solving -0.5714285715 + x = -1.702339327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -1.702339327 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.702339327 + 0.5714285715 x = -1.702339327 + 0.5714285715 Combine like terms: -1.702339327 + 0.5714285715 = -1.1309107555 x = -1.1309107555 Simplifying x = -1.1309107555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2737678985, -1.1309107555}
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