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Simplifying 2x2 + -14x + 49 = 13 Reorder the terms: 49 + -14x + 2x2 = 13 Solving 49 + -14x + 2x2 = 13 Solving for variable 'x'. Reorder the terms: 49 + -13 + -14x + 2x2 = 13 + -13 Combine like terms: 49 + -13 = 36 36 + -14x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 36 + -14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -7x + x2)' equal to zero and attempt to solve: Simplifying 18 + -7x + x2 = 0 Solving 18 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -7x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -7x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -7x + x2 = 0 + -18 -7x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -7x + x2 = -18 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 = -18 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -18 + 12.25 Combine like terms: -18 + 12.25 = -5.75 12.25 + -7x + x2 = -5.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -5.75 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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