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Simplifying 7x2 + 8x + -84 = 0 Reorder the terms: -84 + 8x + 7x2 = 0 Solving -84 + 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'. -12 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 1.142857143x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 1.142857143x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 1.142857143x + x2 = 0 + 12 1.142857143x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 1.142857143x + x2 = 12 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 = 12 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 12 + 0.3265306123 Combine like terms: 12 + 0.3265306123 = 12.3265306123 0.3265306123 + 1.142857143x + x2 = 12.3265306123 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 12.3265306123 Calculate the square root of the right side: 3.510915922 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 3.510915922 and -3.510915922.Subproblem 1
x + 0.5714285715 = 3.510915922 Simplifying x + 0.5714285715 = 3.510915922 Reorder the terms: 0.5714285715 + x = 3.510915922 Solving 0.5714285715 + x = 3.510915922 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 = 3.510915922 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 3.510915922 + -0.5714285715 x = 3.510915922 + -0.5714285715 Combine like terms: 3.510915922 + -0.5714285715 = 2.9394873505 x = 2.9394873505 Simplifying x = 2.9394873505Subproblem 2
x + 0.5714285715 = -3.510915922 Simplifying x + 0.5714285715 = -3.510915922 Reorder the terms: 0.5714285715 + x = -3.510915922 Solving 0.5714285715 + x = -3.510915922 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 = -3.510915922 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -3.510915922 + -0.5714285715 x = -3.510915922 + -0.5714285715 Combine like terms: -3.510915922 + -0.5714285715 = -4.0823444935 x = -4.0823444935 Simplifying x = -4.0823444935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9394873505, -4.0823444935}
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