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Simplifying 30x2 + -8x + 14 = 0 Reorder the terms: 14 + -8x + 30x2 = 0 Solving 14 + -8x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -4x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -4x + 15x2)' equal to zero and attempt to solve: Simplifying 7 + -4x + 15x2 = 0 Solving 7 + -4x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.4666666667 + -0.2666666667x + x2 = 0 Move the constant term to the right: Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.2666666667x + -0.4666666667 + x2 = 0 + -0.4666666667 Reorder the terms: 0.4666666667 + -0.4666666667 + -0.2666666667x + x2 = 0 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + -0.2666666667x + x2 = 0 + -0.4666666667 -0.2666666667x + x2 = 0 + -0.4666666667 Combine like terms: 0 + -0.4666666667 = -0.4666666667 -0.2666666667x + x2 = -0.4666666667 The x term is -0.2666666667x. Take half its coefficient (-0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. -0.2666666667x + 0.01777777780 + x2 = -0.4666666667 + 0.01777777780 Reorder the terms: 0.01777777780 + -0.2666666667x + x2 = -0.4666666667 + 0.01777777780 Combine like terms: -0.4666666667 + 0.01777777780 = -0.4488888889 0.01777777780 + -0.2666666667x + x2 = -0.4488888889 Factor a perfect square on the left side: (x + -0.1333333334)(x + -0.1333333334) = -0.4488888889 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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