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Simplifying 7(x)(x + 2) = 29 Reorder the terms: 7x(2 + x) = 29 (2 * 7x + x * 7x) = 29 (14x + 7x2) = 29 Solving 14x + 7x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 14x + 7x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.142857143 + 2x + x2 = 0 Move the constant term to the right: Add '4.142857143' to each side of the equation. -4.142857143 + 2x + 4.142857143 + x2 = 0 + 4.142857143 Reorder the terms: -4.142857143 + 4.142857143 + 2x + x2 = 0 + 4.142857143 Combine like terms: -4.142857143 + 4.142857143 = 0.000000000 0.000000000 + 2x + x2 = 0 + 4.142857143 2x + x2 = 0 + 4.142857143 Combine like terms: 0 + 4.142857143 = 4.142857143 2x + x2 = 4.142857143 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 4.142857143 + 1 Reorder the terms: 1 + 2x + x2 = 4.142857143 + 1 Combine like terms: 4.142857143 + 1 = 5.142857143 1 + 2x + x2 = 5.142857143 Factor a perfect square on the left side: (x + 1)(x + 1) = 5.142857143 Calculate the square root of the right side: 2.267786838 Break this problem into two subproblems by setting (x + 1) equal to 2.267786838 and -2.267786838.Subproblem 1
x + 1 = 2.267786838 Simplifying x + 1 = 2.267786838 Reorder the terms: 1 + x = 2.267786838 Solving 1 + x = 2.267786838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.267786838 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.267786838 + -1 x = 2.267786838 + -1 Combine like terms: 2.267786838 + -1 = 1.267786838 x = 1.267786838 Simplifying x = 1.267786838Subproblem 2
x + 1 = -2.267786838 Simplifying x + 1 = -2.267786838 Reorder the terms: 1 + x = -2.267786838 Solving 1 + x = -2.267786838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.267786838 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.267786838 + -1 x = -2.267786838 + -1 Combine like terms: -2.267786838 + -1 = -3.267786838 x = -3.267786838 Simplifying x = -3.267786838Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.267786838, -3.267786838}
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