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Simplifying 4x2 + 1 = 4x + -15 Reorder the terms: 1 + 4x2 = 4x + -15 Reorder the terms: 1 + 4x2 = -15 + 4x Solving 1 + 4x2 = -15 + 4x Solving for variable 'x'. Reorder the terms: 1 + 15 + -4x + 4x2 = -15 + 4x + 15 + -4x Combine like terms: 1 + 15 = 16 16 + -4x + 4x2 = -15 + 4x + 15 + -4x Reorder the terms: 16 + -4x + 4x2 = -15 + 15 + 4x + -4x Combine like terms: -15 + 15 = 0 16 + -4x + 4x2 = 0 + 4x + -4x 16 + -4x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 16 + -4x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -1x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -1x + x2)' equal to zero and attempt to solve: Simplifying 4 + -1x + x2 = 0 Solving 4 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x + x2 = 0 + -4 -1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1x + x2 = -4 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 = -4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1x + x2 = -3.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -3.75 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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