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Simplifying 14x2 + 6x + 50 = 0 Reorder the terms: 50 + 6x + 14x2 = 0 Solving 50 + 6x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 3x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying 25 + 3x + 7x2 = 0 Solving 25 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.571428571 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '-3.571428571' to each side of the equation. 3.571428571 + 0.4285714286x + -3.571428571 + x2 = 0 + -3.571428571 Reorder the terms: 3.571428571 + -3.571428571 + 0.4285714286x + x2 = 0 + -3.571428571 Combine like terms: 3.571428571 + -3.571428571 = 0.000000000 0.000000000 + 0.4285714286x + x2 = 0 + -3.571428571 0.4285714286x + x2 = 0 + -3.571428571 Combine like terms: 0 + -3.571428571 = -3.571428571 0.4285714286x + x2 = -3.571428571 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = -3.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = -3.571428571 + 0.04591836735 Combine like terms: -3.571428571 + 0.04591836735 = -3.52551020365 0.04591836735 + 0.4285714286x + x2 = -3.52551020365 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = -3.52551020365 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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