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Simplifying 28x2 + -40x + 11 = 0 Reorder the terms: 11 + -40x + 28x2 = 0 Solving 11 + -40x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.3928571429 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.3928571429' to each side of the equation. 0.3928571429 + -1.428571429x + -0.3928571429 + x2 = 0 + -0.3928571429 Reorder the terms: 0.3928571429 + -0.3928571429 + -1.428571429x + x2 = 0 + -0.3928571429 Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + -0.3928571429 -1.428571429x + x2 = 0 + -0.3928571429 Combine like terms: 0 + -0.3928571429 = -0.3928571429 -1.428571429x + x2 = -0.3928571429 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 = -0.3928571429 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = -0.3928571429 + 0.5102040819 Combine like terms: -0.3928571429 + 0.5102040819 = 0.117346939 0.5102040819 + -1.428571429x + x2 = 0.117346939 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.117346939 Calculate the square root of the right side: 0.342559395 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.342559395 and -0.342559395.Subproblem 1
x + -0.7142857145 = 0.342559395 Simplifying x + -0.7142857145 = 0.342559395 Reorder the terms: -0.7142857145 + x = 0.342559395 Solving -0.7142857145 + x = 0.342559395 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 = 0.342559395 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.342559395 + 0.7142857145 x = 0.342559395 + 0.7142857145 Combine like terms: 0.342559395 + 0.7142857145 = 1.0568451095 x = 1.0568451095 Simplifying x = 1.0568451095Subproblem 2
x + -0.7142857145 = -0.342559395 Simplifying x + -0.7142857145 = -0.342559395 Reorder the terms: -0.7142857145 + x = -0.342559395 Solving -0.7142857145 + x = -0.342559395 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 = -0.342559395 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.342559395 + 0.7142857145 x = -0.342559395 + 0.7142857145 Combine like terms: -0.342559395 + 0.7142857145 = 0.3717263195 x = 0.3717263195 Simplifying x = 0.3717263195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0568451095, 0.3717263195}
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