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Simplifying 7x(x + 3) = 5x + 29 Reorder the terms: 7x(3 + x) = 5x + 29 (3 * 7x + x * 7x) = 5x + 29 (21x + 7x2) = 5x + 29 Reorder the terms: 21x + 7x2 = 29 + 5x Solving 21x + 7x2 = 29 + 5x Solving for variable 'x'. Reorder the terms: -29 + 21x + -5x + 7x2 = 29 + 5x + -29 + -5x Combine like terms: 21x + -5x = 16x -29 + 16x + 7x2 = 29 + 5x + -29 + -5x Reorder the terms: -29 + 16x + 7x2 = 29 + -29 + 5x + -5x Combine like terms: 29 + -29 = 0 -29 + 16x + 7x2 = 0 + 5x + -5x -29 + 16x + 7x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -29 + 16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.142857143 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + 2.285714286x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + 2.285714286x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + 4.142857143 2.285714286x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 2.285714286x + x2 = 4.142857143 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 = 4.142857143 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 4.142857143 + 1.306122449 Combine like terms: 4.142857143 + 1.306122449 = 5.448979592 1.306122449 + 2.285714286x + x2 = 5.448979592 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 5.448979592 Calculate the square root of the right side: 2.334304948 Break this problem into two subproblems by setting (x + 1.142857143) equal to 2.334304948 and -2.334304948.Subproblem 1
x + 1.142857143 = 2.334304948 Simplifying x + 1.142857143 = 2.334304948 Reorder the terms: 1.142857143 + x = 2.334304948 Solving 1.142857143 + x = 2.334304948 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 = 2.334304948 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 2.334304948 + -1.142857143 x = 2.334304948 + -1.142857143 Combine like terms: 2.334304948 + -1.142857143 = 1.191447805 x = 1.191447805 Simplifying x = 1.191447805Subproblem 2
x + 1.142857143 = -2.334304948 Simplifying x + 1.142857143 = -2.334304948 Reorder the terms: 1.142857143 + x = -2.334304948 Solving 1.142857143 + x = -2.334304948 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 = -2.334304948 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -2.334304948 + -1.142857143 x = -2.334304948 + -1.142857143 Combine like terms: -2.334304948 + -1.142857143 = -3.477162091 x = -3.477162091 Simplifying x = -3.477162091Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.191447805, -3.477162091}
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