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Simplifying (7x + 8)(7x + 8) = 10 Reorder the terms: (8 + 7x)(7x + 8) = 10 Reorder the terms: (8 + 7x)(8 + 7x) = 10 Multiply (8 + 7x) * (8 + 7x) (8(8 + 7x) + 7x * (8 + 7x)) = 10 ((8 * 8 + 7x * 8) + 7x * (8 + 7x)) = 10 ((64 + 56x) + 7x * (8 + 7x)) = 10 (64 + 56x + (8 * 7x + 7x * 7x)) = 10 (64 + 56x + (56x + 49x2)) = 10 Combine like terms: 56x + 56x = 112x (64 + 112x + 49x2) = 10 Solving 64 + 112x + 49x2 = 10 Solving for variable 'x'. Reorder the terms: 64 + -10 + 112x + 49x2 = 10 + -10 Combine like terms: 64 + -10 = 54 54 + 112x + 49x2 = 10 + -10 Combine like terms: 10 + -10 = 0 54 + 112x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 1.102040816 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '-1.102040816' to each side of the equation. 1.102040816 + 2.285714286x + -1.102040816 + x2 = 0 + -1.102040816 Reorder the terms: 1.102040816 + -1.102040816 + 2.285714286x + x2 = 0 + -1.102040816 Combine like terms: 1.102040816 + -1.102040816 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + -1.102040816 2.285714286x + x2 = 0 + -1.102040816 Combine like terms: 0 + -1.102040816 = -1.102040816 2.285714286x + x2 = -1.102040816 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = -1.102040816 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = -1.102040816 + 1.306122449 Combine like terms: -1.102040816 + 1.306122449 = 0.204081633 1.306122449 + 2.285714286x + x2 = 0.204081633 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 0.204081633 Calculate the square root of the right side: 0.451753952 Break this problem into two subproblems by setting (x + 1.142857143) equal to 0.451753952 and -0.451753952.Subproblem 1
x + 1.142857143 = 0.451753952 Simplifying x + 1.142857143 = 0.451753952 Reorder the terms: 1.142857143 + x = 0.451753952 Solving 1.142857143 + x = 0.451753952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = 0.451753952 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 0.451753952 + -1.142857143 x = 0.451753952 + -1.142857143 Combine like terms: 0.451753952 + -1.142857143 = -0.691103191 x = -0.691103191 Simplifying x = -0.691103191Subproblem 2
x + 1.142857143 = -0.451753952 Simplifying x + 1.142857143 = -0.451753952 Reorder the terms: 1.142857143 + x = -0.451753952 Solving 1.142857143 + x = -0.451753952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = -0.451753952 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -0.451753952 + -1.142857143 x = -0.451753952 + -1.142857143 Combine like terms: -0.451753952 + -1.142857143 = -1.594611095 x = -1.594611095 Simplifying x = -1.594611095Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.691103191, -1.594611095}
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