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Simplifying 41 + -2x(8 + -7x) = 31 + 4 41 + (8 * -2x + -7x * -2x) = 31 + 4 41 + (-16x + 14x2) = 31 + 4 Combine like terms: 31 + 4 = 35 41 + -16x + 14x2 = 35 Solving 41 + -16x + 14x2 = 35 Solving for variable 'x'. Reorder the terms: 41 + -35 + -16x + 14x2 = 35 + -35 Combine like terms: 41 + -35 = 6 6 + -16x + 14x2 = 35 + -35 Combine like terms: 35 + -35 = 0 6 + -16x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -8x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -8x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + -8x + 7x2 = 0 Solving 3 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -1.142857143x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -1.142857143x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + -0.4285714286 -1.142857143x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -1.142857143x + x2 = -0.4285714286 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = -0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = -0.4285714286 + 0.3265306123 Combine like terms: -0.4285714286 + 0.3265306123 = -0.1020408163 0.3265306123 + -1.142857143x + x2 = -0.1020408163 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = -0.1020408163 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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