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Simplifying 2x2 + -2x + 7 = 5 Reorder the terms: 7 + -2x + 2x2 = 5 Solving 7 + -2x + 2x2 = 5 Solving for variable 'x'. Reorder the terms: 7 + -5 + -2x + 2x2 = 5 + -5 Combine like terms: 7 + -5 = 2 2 + -2x + 2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 2 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1x + x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + x2 = 0 Solving 1 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 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 = -1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1x + x2 = -0.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.75 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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