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Simplifying 2(x2 + -7x + 21) = 0 Reorder the terms: 2(21 + -7x + x2) = 0 (21 * 2 + -7x * 2 + x2 * 2) = 0 (42 + -14x + 2x2) = 0 Solving 42 + -14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -7x + x2)' equal to zero and attempt to solve: Simplifying 21 + -7x + x2 = 0 Solving 21 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -7x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -7x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -7x + x2 = 0 + -21 -7x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -7x + x2 = -21 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 = -21 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -21 + 12.25 Combine like terms: -21 + 12.25 = -8.75 12.25 + -7x + x2 = -8.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -8.75 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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