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Simplifying 7x2 + 63x + 116 = 0 Reorder the terms: 116 + 63x + 7x2 = 0 Solving 116 + 63x + 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'. 16.57142857 + 9x + x2 = 0 Move the constant term to the right: Add '-16.57142857' to each side of the equation. 16.57142857 + 9x + -16.57142857 + x2 = 0 + -16.57142857 Reorder the terms: 16.57142857 + -16.57142857 + 9x + x2 = 0 + -16.57142857 Combine like terms: 16.57142857 + -16.57142857 = 0.00000000 0.00000000 + 9x + x2 = 0 + -16.57142857 9x + x2 = 0 + -16.57142857 Combine like terms: 0 + -16.57142857 = -16.57142857 9x + x2 = -16.57142857 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -16.57142857 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -16.57142857 + 20.25 Combine like terms: -16.57142857 + 20.25 = 3.67857143 20.25 + 9x + x2 = 3.67857143 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 3.67857143 Calculate the square root of the right side: 1.917960226 Break this problem into two subproblems by setting (x + 4.5) equal to 1.917960226 and -1.917960226.Subproblem 1
x + 4.5 = 1.917960226 Simplifying x + 4.5 = 1.917960226 Reorder the terms: 4.5 + x = 1.917960226 Solving 4.5 + x = 1.917960226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 1.917960226 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 1.917960226 + -4.5 x = 1.917960226 + -4.5 Combine like terms: 1.917960226 + -4.5 = -2.582039774 x = -2.582039774 Simplifying x = -2.582039774Subproblem 2
x + 4.5 = -1.917960226 Simplifying x + 4.5 = -1.917960226 Reorder the terms: 4.5 + x = -1.917960226 Solving 4.5 + x = -1.917960226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -1.917960226 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -1.917960226 + -4.5 x = -1.917960226 + -4.5 Combine like terms: -1.917960226 + -4.5 = -6.417960226 x = -6.417960226 Simplifying x = -6.417960226Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.582039774, -6.417960226}
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