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Simplifying 7x(x + 4) = 8 Reorder the terms: 7x(4 + x) = 8 (4 * 7x + x * 7x) = 8 (28x + 7x2) = 8 Solving 28x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 28x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 28x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 4x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 4x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 4x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 4x + x2 = 0 + 1.142857143 4x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 4x + x2 = 1.142857143 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.142857143 + 4 Reorder the terms: 4 + 4x + x2 = 1.142857143 + 4 Combine like terms: 1.142857143 + 4 = 5.142857143 4 + 4x + x2 = 5.142857143 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.142857143 Calculate the square root of the right side: 2.267786838 Break this problem into two subproblems by setting (x + 2) equal to 2.267786838 and -2.267786838.Subproblem 1
x + 2 = 2.267786838 Simplifying x + 2 = 2.267786838 Reorder the terms: 2 + x = 2.267786838 Solving 2 + x = 2.267786838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.267786838 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.267786838 + -2 x = 2.267786838 + -2 Combine like terms: 2.267786838 + -2 = 0.267786838 x = 0.267786838 Simplifying x = 0.267786838Subproblem 2
x + 2 = -2.267786838 Simplifying x + 2 = -2.267786838 Reorder the terms: 2 + x = -2.267786838 Solving 2 + x = -2.267786838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.267786838 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.267786838 + -2 x = -2.267786838 + -2 Combine like terms: -2.267786838 + -2 = -4.267786838 x = -4.267786838 Simplifying x = -4.267786838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.267786838, -4.267786838}
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