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Simplifying -14x2 + -16x + -420 = 0 Reorder the terms: -420 + -16x + -14x2 = 0 Solving -420 + -16x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(210 + 8x + 7x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(210 + 8x + 7x2)' equal to zero and attempt to solve: Simplifying 210 + 8x + 7x2 = 0 Solving 210 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 30 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + 1.142857143x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 1.142857143x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 1.142857143x + x2 = 0 + -30 1.142857143x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 1.142857143x + x2 = -30 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 = -30 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = -30 + 0.3265306123 Combine like terms: -30 + 0.3265306123 = -29.6734693877 0.3265306123 + 1.142857143x + x2 = -29.6734693877 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = -29.6734693877 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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