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Simplifying 7x2 + 14x = 8 Reorder the terms: 14x + 7x2 = 8 Solving 14x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 14x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 2x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 2x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 2x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 2x + x2 = 0 + 1.142857143 2x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 2x + x2 = 1.142857143 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 = 1.142857143 + 1 Reorder the terms: 1 + 2x + x2 = 1.142857143 + 1 Combine like terms: 1.142857143 + 1 = 2.142857143 1 + 2x + x2 = 2.142857143 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.142857143 Calculate the square root of the right side: 1.463850109 Break this problem into two subproblems by setting (x + 1) equal to 1.463850109 and -1.463850109.Subproblem 1
x + 1 = 1.463850109 Simplifying x + 1 = 1.463850109 Reorder the terms: 1 + x = 1.463850109 Solving 1 + x = 1.463850109 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 = 1.463850109 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.463850109 + -1 x = 1.463850109 + -1 Combine like terms: 1.463850109 + -1 = 0.463850109 x = 0.463850109 Simplifying x = 0.463850109Subproblem 2
x + 1 = -1.463850109 Simplifying x + 1 = -1.463850109 Reorder the terms: 1 + x = -1.463850109 Solving 1 + x = -1.463850109 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 = -1.463850109 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.463850109 + -1 x = -1.463850109 + -1 Combine like terms: -1.463850109 + -1 = -2.463850109 x = -2.463850109 Simplifying x = -2.463850109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.463850109, -2.463850109}
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