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Simplifying 0 = -16(x2 + 2x + 3) Reorder the terms: 0 = -16(3 + 2x + x2) 0 = (3 * -16 + 2x * -16 + x2 * -16) 0 = (-48 + -32x + -16x2) Solving 0 = -48 + -32x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 48 = 48 48 + 32x + 16x2 = -48 + -32x + -16x2 + 48 + 32x + 16x2 Reorder the terms: 48 + 32x + 16x2 = -48 + 48 + -32x + 32x + -16x2 + 16x2 Combine like terms: -48 + 48 = 0 48 + 32x + 16x2 = 0 + -32x + 32x + -16x2 + 16x2 48 + 32x + 16x2 = -32x + 32x + -16x2 + 16x2 Combine like terms: -32x + 32x = 0 48 + 32x + 16x2 = 0 + -16x2 + 16x2 48 + 32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 48 + 32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(3 + 2x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + 2x + x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + x2 = 0 Solving 3 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + x2 = 0 + -3 2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x + x2 = -3 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 = -3 + 1 Reorder the terms: 1 + 2x + x2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2x + x2 = -2 Factor a perfect square on the left side: (x + 1)(x + 1) = -2 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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