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Simplifying (7x + -5)(7x + -5) = 38 Reorder the terms: (-5 + 7x)(7x + -5) = 38 Reorder the terms: (-5 + 7x)(-5 + 7x) = 38 Multiply (-5 + 7x) * (-5 + 7x) (-5(-5 + 7x) + 7x * (-5 + 7x)) = 38 ((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) = 38 ((25 + -35x) + 7x * (-5 + 7x)) = 38 (25 + -35x + (-5 * 7x + 7x * 7x)) = 38 (25 + -35x + (-35x + 49x2)) = 38 Combine like terms: -35x + -35x = -70x (25 + -70x + 49x2) = 38 Solving 25 + -70x + 49x2 = 38 Solving for variable 'x'. Reorder the terms: 25 + -38 + -70x + 49x2 = 38 + -38 Combine like terms: 25 + -38 = -13 -13 + -70x + 49x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -13 + -70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.2653061224 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '0.2653061224' to each side of the equation. -0.2653061224 + -1.428571429x + 0.2653061224 + x2 = 0 + 0.2653061224 Reorder the terms: -0.2653061224 + 0.2653061224 + -1.428571429x + x2 = 0 + 0.2653061224 Combine like terms: -0.2653061224 + 0.2653061224 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + 0.2653061224 -1.428571429x + x2 = 0 + 0.2653061224 Combine like terms: 0 + 0.2653061224 = 0.2653061224 -1.428571429x + x2 = 0.2653061224 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 = 0.2653061224 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 0.2653061224 + 0.5102040819 Combine like terms: 0.2653061224 + 0.5102040819 = 0.7755102043 0.5102040819 + -1.428571429x + x2 = 0.7755102043 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.7755102043 Calculate the square root of the right side: 0.880630572 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.880630572 and -0.880630572.Subproblem 1
x + -0.7142857145 = 0.880630572 Simplifying x + -0.7142857145 = 0.880630572 Reorder the terms: -0.7142857145 + x = 0.880630572 Solving -0.7142857145 + x = 0.880630572 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 = 0.880630572 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.880630572 + 0.7142857145 x = 0.880630572 + 0.7142857145 Combine like terms: 0.880630572 + 0.7142857145 = 1.5949162865 x = 1.5949162865 Simplifying x = 1.5949162865Subproblem 2
x + -0.7142857145 = -0.880630572 Simplifying x + -0.7142857145 = -0.880630572 Reorder the terms: -0.7142857145 + x = -0.880630572 Solving -0.7142857145 + x = -0.880630572 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 = -0.880630572 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.880630572 + 0.7142857145 x = -0.880630572 + 0.7142857145 Combine like terms: -0.880630572 + 0.7142857145 = -0.1663448575 x = -0.1663448575 Simplifying x = -0.1663448575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5949162865, -0.1663448575}
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