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Simplifying 7x2 + 7x + -130 = 0 Reorder the terms: -130 + 7x + 7x2 = 0 Solving -130 + 7x + 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'. -18.57142857 + x + x2 = 0 Move the constant term to the right: Add '18.57142857' to each side of the equation. -18.57142857 + x + 18.57142857 + x2 = 0 + 18.57142857 Reorder the terms: -18.57142857 + 18.57142857 + x + x2 = 0 + 18.57142857 Combine like terms: -18.57142857 + 18.57142857 = 0.00000000 0.00000000 + x + x2 = 0 + 18.57142857 x + x2 = 0 + 18.57142857 Combine like terms: 0 + 18.57142857 = 18.57142857 x + x2 = 18.57142857 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 18.57142857 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 18.57142857 + 0.25 Combine like terms: 18.57142857 + 0.25 = 18.82142857 1.25 + x2 = 18.82142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.82142857 Calculate the square root of the right side: 4.33836704 Break this problem into two subproblems by setting (x + 0.5) equal to 4.33836704 and -4.33836704.Subproblem 1
x + 0.5 = 4.33836704 Simplifying x + 0.5 = 4.33836704 Reorder the terms: 0.5 + x = 4.33836704 Solving 0.5 + x = 4.33836704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.33836704 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.33836704 + -0.5 x = 4.33836704 + -0.5 Combine like terms: 4.33836704 + -0.5 = 3.83836704 x = 3.83836704 Simplifying x = 3.83836704Subproblem 2
x + 0.5 = -4.33836704 Simplifying x + 0.5 = -4.33836704 Reorder the terms: 0.5 + x = -4.33836704 Solving 0.5 + x = -4.33836704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.33836704 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.33836704 + -0.5 x = -4.33836704 + -0.5 Combine like terms: -4.33836704 + -0.5 = -4.83836704 x = -4.83836704 Simplifying x = -4.83836704Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.83836704, -4.83836704}
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