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Simplifying 12(x2 + -7x + 14) = 0 Reorder the terms: 12(14 + -7x + x2) = 0 (14 * 12 + -7x * 12 + x2 * 12) = 0 (168 + -84x + 12x2) = 0 Solving 168 + -84x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(14 + -7x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(14 + -7x + x2)' equal to zero and attempt to solve: Simplifying 14 + -7x + x2 = 0 Solving 14 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -7x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -7x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -7x + x2 = 0 + -14 -7x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -7x + x2 = -14 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -14 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -14 + 12.25 Combine like terms: -14 + 12.25 = -1.75 12.25 + -7x + x2 = -1.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -1.75 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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