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Simplifying (7x + -5)(7x + -5) + -10 = 0 Reorder the terms: (-5 + 7x)(7x + -5) + -10 = 0 Reorder the terms: (-5 + 7x)(-5 + 7x) + -10 = 0 Multiply (-5 + 7x) * (-5 + 7x) (-5(-5 + 7x) + 7x * (-5 + 7x)) + -10 = 0 ((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) + -10 = 0 ((25 + -35x) + 7x * (-5 + 7x)) + -10 = 0 (25 + -35x + (-5 * 7x + 7x * 7x)) + -10 = 0 (25 + -35x + (-35x + 49x2)) + -10 = 0 Combine like terms: -35x + -35x = -70x (25 + -70x + 49x2) + -10 = 0 Reorder the terms: 25 + -10 + -70x + 49x2 = 0 Combine like terms: 25 + -10 = 15 15 + -70x + 49x2 = 0 Solving 15 + -70x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.306122449 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.306122449' to each side of the equation. 0.306122449 + -1.428571429x + -0.306122449 + x2 = 0 + -0.306122449 Reorder the terms: 0.306122449 + -0.306122449 + -1.428571429x + x2 = 0 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + -0.306122449 -1.428571429x + x2 = 0 + -0.306122449 Combine like terms: 0 + -0.306122449 = -0.306122449 -1.428571429x + x2 = -0.306122449 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = -0.306122449 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = -0.306122449 + 0.5102040819 Combine like terms: -0.306122449 + 0.5102040819 = 0.2040816329 0.5102040819 + -1.428571429x + x2 = 0.2040816329 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.2040816329 Calculate the square root of the right side: 0.451753952 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.451753952 and -0.451753952.Subproblem 1
x + -0.7142857145 = 0.451753952 Simplifying x + -0.7142857145 = 0.451753952 Reorder the terms: -0.7142857145 + x = 0.451753952 Solving -0.7142857145 + x = 0.451753952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.451753952 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.451753952 + 0.7142857145 x = 0.451753952 + 0.7142857145 Combine like terms: 0.451753952 + 0.7142857145 = 1.1660396665 x = 1.1660396665 Simplifying x = 1.1660396665Subproblem 2
x + -0.7142857145 = -0.451753952 Simplifying x + -0.7142857145 = -0.451753952 Reorder the terms: -0.7142857145 + x = -0.451753952 Solving -0.7142857145 + x = -0.451753952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.451753952 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.451753952 + 0.7142857145 x = -0.451753952 + 0.7142857145 Combine like terms: -0.451753952 + 0.7142857145 = 0.2625317625 x = 0.2625317625 Simplifying x = 0.2625317625Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1660396665, 0.2625317625}
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