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Simplifying -1x2 = 4x + 21 Reorder the terms: -1x2 = 21 + 4x Solving -1x2 = 21 + 4x Solving for variable 'x'. Reorder the terms: -21 + -4x + -1x2 = 21 + 4x + -21 + -4x Reorder the terms: -21 + -4x + -1x2 = 21 + -21 + 4x + -4x Combine like terms: 21 + -21 = 0 -21 + -4x + -1x2 = 0 + 4x + -4x -21 + -4x + -1x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -21 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 4x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 4x + x2)' equal to zero and attempt to solve: Simplifying 21 + 4x + x2 = 0 Solving 21 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 4x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 4x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 4x + x2 = 0 + -21 4x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 4x + x2 = -21 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -21 + 4 Reorder the terms: 4 + 4x + x2 = -21 + 4 Combine like terms: -21 + 4 = -17 4 + 4x + x2 = -17 Factor a perfect square on the left side: (x + 2)(x + 2) = -17 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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