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Simplifying 56x2 + 22x + -40 = 0 Reorder the terms: -40 + 22x + 56x2 = 0 Solving -40 + 22x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 11x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 11x + 28x2)' equal to zero and attempt to solve: Simplifying -20 + 11x + 28x2 = 0 Solving -20 + 11x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.7142857143 + 0.3928571429x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.3928571429x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.3928571429x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.3928571429x + x2 = 0 + 0.7142857143 0.3928571429x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.3928571429x + x2 = 0.7142857143 The x term is 0.3928571429x. Take half its coefficient (0.1964285715). Square it (0.03858418370) and add it to both sides. Add '0.03858418370' to each side of the equation. 0.3928571429x + 0.03858418370 + x2 = 0.7142857143 + 0.03858418370 Reorder the terms: 0.03858418370 + 0.3928571429x + x2 = 0.7142857143 + 0.03858418370 Combine like terms: 0.7142857143 + 0.03858418370 = 0.752869898 0.03858418370 + 0.3928571429x + x2 = 0.752869898 Factor a perfect square on the left side: (x + 0.1964285715)(x + 0.1964285715) = 0.752869898 Calculate the square root of the right side: 0.867680758 Break this problem into two subproblems by setting (x + 0.1964285715) equal to 0.867680758 and -0.867680758.Subproblem 1
x + 0.1964285715 = 0.867680758 Simplifying x + 0.1964285715 = 0.867680758 Reorder the terms: 0.1964285715 + x = 0.867680758 Solving 0.1964285715 + x = 0.867680758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1964285715' to each side of the equation. 0.1964285715 + -0.1964285715 + x = 0.867680758 + -0.1964285715 Combine like terms: 0.1964285715 + -0.1964285715 = 0.0000000000 0.0000000000 + x = 0.867680758 + -0.1964285715 x = 0.867680758 + -0.1964285715 Combine like terms: 0.867680758 + -0.1964285715 = 0.6712521865 x = 0.6712521865 Simplifying x = 0.6712521865Subproblem 2
x + 0.1964285715 = -0.867680758 Simplifying x + 0.1964285715 = -0.867680758 Reorder the terms: 0.1964285715 + x = -0.867680758 Solving 0.1964285715 + x = -0.867680758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1964285715' to each side of the equation. 0.1964285715 + -0.1964285715 + x = -0.867680758 + -0.1964285715 Combine like terms: 0.1964285715 + -0.1964285715 = 0.0000000000 0.0000000000 + x = -0.867680758 + -0.1964285715 x = -0.867680758 + -0.1964285715 Combine like terms: -0.867680758 + -0.1964285715 = -1.0641093295 x = -1.0641093295 Simplifying x = -1.0641093295Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6712521865, -1.0641093295}Solution
x = {0.6712521865, -1.0641093295}
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