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Simplifying 7x + 7 = 7x(x + 8) + -8 Reorder the terms: 7 + 7x = 7x(x + 8) + -8 Reorder the terms: 7 + 7x = 7x(8 + x) + -8 7 + 7x = (8 * 7x + x * 7x) + -8 7 + 7x = (56x + 7x2) + -8 Reorder the terms: 7 + 7x = -8 + 56x + 7x2 Solving 7 + 7x = -8 + 56x + 7x2 Solving for variable 'x'. Reorder the terms: 7 + 8 + 7x + -56x + -7x2 = -8 + 56x + 7x2 + 8 + -56x + -7x2 Combine like terms: 7 + 8 = 15 15 + 7x + -56x + -7x2 = -8 + 56x + 7x2 + 8 + -56x + -7x2 Combine like terms: 7x + -56x = -49x 15 + -49x + -7x2 = -8 + 56x + 7x2 + 8 + -56x + -7x2 Reorder the terms: 15 + -49x + -7x2 = -8 + 8 + 56x + -56x + 7x2 + -7x2 Combine like terms: -8 + 8 = 0 15 + -49x + -7x2 = 0 + 56x + -56x + 7x2 + -7x2 15 + -49x + -7x2 = 56x + -56x + 7x2 + -7x2 Combine like terms: 56x + -56x = 0 15 + -49x + -7x2 = 0 + 7x2 + -7x2 15 + -49x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 15 + -49x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.142857143 + 7x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 7x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 7x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 7x + x2 = 0 + 2.142857143 7x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 7x + x2 = 2.142857143 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 = 2.142857143 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 2.142857143 + 12.25 Combine like terms: 2.142857143 + 12.25 = 14.392857143 12.25 + 7x + x2 = 14.392857143 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 14.392857143 Calculate the square root of the right side: 3.793791921 Break this problem into two subproblems by setting (x + 3.5) equal to 3.793791921 and -3.793791921.Subproblem 1
x + 3.5 = 3.793791921 Simplifying x + 3.5 = 3.793791921 Reorder the terms: 3.5 + x = 3.793791921 Solving 3.5 + x = 3.793791921 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 = 3.793791921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.793791921 + -3.5 x = 3.793791921 + -3.5 Combine like terms: 3.793791921 + -3.5 = 0.293791921 x = 0.293791921 Simplifying x = 0.293791921Subproblem 2
x + 3.5 = -3.793791921 Simplifying x + 3.5 = -3.793791921 Reorder the terms: 3.5 + x = -3.793791921 Solving 3.5 + x = -3.793791921 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 = -3.793791921 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.793791921 + -3.5 x = -3.793791921 + -3.5 Combine like terms: -3.793791921 + -3.5 = -7.293791921 x = -7.293791921 Simplifying x = -7.293791921Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293791921, -7.293791921}
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