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Simplifying x(7x + 1) = 5 Reorder the terms: x(1 + 7x) = 5 (1 * x + 7x * x) = 5 (1x + 7x2) = 5 Solving 1x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 1x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.1428571429x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.1428571429x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + 0.7142857143 0.1428571429x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.1428571429x + x2 = 0.7142857143 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 0.7142857143 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 0.7142857143 + 0.005102040819 Combine like terms: 0.7142857143 + 0.005102040819 = 0.719387755119 0.005102040819 + 0.1428571429x + x2 = 0.719387755119 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 0.719387755119 Calculate the square root of the right side: 0.848167292 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 0.848167292 and -0.848167292.Subproblem 1
x + 0.07142857145 = 0.848167292 Simplifying x + 0.07142857145 = 0.848167292 Reorder the terms: 0.07142857145 + x = 0.848167292 Solving 0.07142857145 + x = 0.848167292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 0.848167292 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 0.848167292 + -0.07142857145 x = 0.848167292 + -0.07142857145 Combine like terms: 0.848167292 + -0.07142857145 = 0.77673872055 x = 0.77673872055 Simplifying x = 0.77673872055Subproblem 2
x + 0.07142857145 = -0.848167292 Simplifying x + 0.07142857145 = -0.848167292 Reorder the terms: 0.07142857145 + x = -0.848167292 Solving 0.07142857145 + x = -0.848167292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -0.848167292 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -0.848167292 + -0.07142857145 x = -0.848167292 + -0.07142857145 Combine like terms: -0.848167292 + -0.07142857145 = -0.91959586345 x = -0.91959586345 Simplifying x = -0.91959586345Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.77673872055, -0.91959586345}
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