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Simplifying 7x(x + 7) = 116 Reorder the terms: 7x(7 + x) = 116 (7 * 7x + x * 7x) = 116 (49x + 7x2) = 116 Solving 49x + 7x2 = 116 Solving for variable 'x'. Reorder the terms: -116 + 49x + 7x2 = 116 + -116 Combine like terms: 116 + -116 = 0 -116 + 49x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -16.57142857 + 7x + x2 = 0 Move the constant term to the right: Add '16.57142857' to each side of the equation. -16.57142857 + 7x + 16.57142857 + x2 = 0 + 16.57142857 Reorder the terms: -16.57142857 + 16.57142857 + 7x + x2 = 0 + 16.57142857 Combine like terms: -16.57142857 + 16.57142857 = 0.00000000 0.00000000 + 7x + x2 = 0 + 16.57142857 7x + x2 = 0 + 16.57142857 Combine like terms: 0 + 16.57142857 = 16.57142857 7x + x2 = 16.57142857 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 16.57142857 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 16.57142857 + 12.25 Combine like terms: 16.57142857 + 12.25 = 28.82142857 12.25 + 7x + x2 = 28.82142857 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 28.82142857 Calculate the square root of the right side: 5.368559264 Break this problem into two subproblems by setting (x + 3.5) equal to 5.368559264 and -5.368559264.Subproblem 1
x + 3.5 = 5.368559264 Simplifying x + 3.5 = 5.368559264 Reorder the terms: 3.5 + x = 5.368559264 Solving 3.5 + x = 5.368559264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.368559264 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.368559264 + -3.5 x = 5.368559264 + -3.5 Combine like terms: 5.368559264 + -3.5 = 1.868559264 x = 1.868559264 Simplifying x = 1.868559264Subproblem 2
x + 3.5 = -5.368559264 Simplifying x + 3.5 = -5.368559264 Reorder the terms: 3.5 + x = -5.368559264 Solving 3.5 + x = -5.368559264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.368559264 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.368559264 + -3.5 x = -5.368559264 + -3.5 Combine like terms: -5.368559264 + -3.5 = -8.868559264 x = -8.868559264 Simplifying x = -8.868559264Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.868559264, -8.868559264}
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