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Simplifying -1x2 + -2x + 3 = 21 Reorder the terms: 3 + -2x + -1x2 = 21 Solving 3 + -2x + -1x2 = 21 Solving for variable 'x'. Reorder the terms: 3 + -21 + -2x + -1x2 = 21 + -21 Combine like terms: 3 + -21 = -18 -18 + -2x + -1x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -18 + -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 2x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + 2x + x2)' equal to zero and attempt to solve: Simplifying 18 + 2x + x2 = 0 Solving 18 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 2x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 2x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 2x + x2 = 0 + -18 2x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 2x + x2 = -18 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -18 + 1 Reorder the terms: 1 + 2x + x2 = -18 + 1 Combine like terms: -18 + 1 = -17 1 + 2x + x2 = -17 Factor a perfect square on the left side: (x + 1)(x + 1) = -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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