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Simplifying -16(x2 + 6x + 84) = 0 Reorder the terms: -16(84 + 6x + x2) = 0 (84 * -16 + 6x * -16 + x2 * -16) = 0 (-1344 + -96x + -16x2) = 0 Solving -1344 + -96x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-16'. -16(84 + 6x + x2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(84 + 6x + x2)' equal to zero and attempt to solve: Simplifying 84 + 6x + x2 = 0 Solving 84 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 6x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 6x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 6x + x2 = 0 + -84 6x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 6x + x2 = -84 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -84 + 9 Reorder the terms: 9 + 6x + x2 = -84 + 9 Combine like terms: -84 + 9 = -75 9 + 6x + x2 = -75 Factor a perfect square on the left side: (x + 3)(x + 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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