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Simplifying 7x2 + -7x + 196 = 0 Reorder the terms: 196 + -7x + 7x2 = 0 Solving 196 + -7x + 7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(28 + -1x + x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(28 + -1x + x2)' equal to zero and attempt to solve: Simplifying 28 + -1x + x2 = 0 Solving 28 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -1x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -1x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -1x + x2 = 0 + -28 -1x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -1x + x2 = -28 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -28 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -28 + 0.25 Combine like terms: -28 + 0.25 = -27.75 0.25 + -1x + x2 = -27.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -27.75 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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