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Simplifying -16(x2 + -2x + 20.25) + -324 = 0 Reorder the terms: -16(20.25 + -2x + x2) + -324 = 0 (20.25 * -16 + -2x * -16 + x2 * -16) + -324 = 0 (-324 + 32x + -16x2) + -324 = 0 Reorder the terms: -324 + -324 + 32x + -16x2 = 0 Combine like terms: -324 + -324 = -648 -648 + 32x + -16x2 = 0 Solving -648 + 32x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-81 + 4x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-81 + 4x + -2x2)' equal to zero and attempt to solve: Simplifying -81 + 4x + -2x2 = 0 Solving -81 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 40.5 + -2x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + -2x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + -2x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + -2x + x2 = 0 + -40.5 -2x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 -2x + x2 = -40.5 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 = -40.5 + 1 Reorder the terms: 1 + -2x + x2 = -40.5 + 1 Combine like terms: -40.5 + 1 = -39.5 1 + -2x + x2 = -39.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -39.5 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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