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Simplifying 2(6x2 + -24x + 25) = 0 Reorder the terms: 2(25 + -24x + 6x2) = 0 (25 * 2 + -24x * 2 + 6x2 * 2) = 0 (50 + -48x + 12x2) = 0 Solving 50 + -48x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -24x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -24x + 6x2)' equal to zero and attempt to solve: Simplifying 25 + -24x + 6x2 = 0 Solving 25 + -24x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.166666667 + -4x + x2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + -4x + -4.166666667 + x2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + -4x + x2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -4.166666667 -4x + x2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 -4x + x2 = -4.166666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -4.166666667 + 4 Reorder the terms: 4 + -4x + x2 = -4.166666667 + 4 Combine like terms: -4.166666667 + 4 = -0.166666667 4 + -4x + x2 = -0.166666667 Factor a perfect square on the left side: (x + -2)(x + -2) = -0.166666667 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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