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Simplifying (400 + -100X)(32 + X) = 129600 Multiply (400 + -100X) * (32 + X) (400(32 + X) + -100X * (32 + X)) = 129600 ((32 * 400 + X * 400) + -100X * (32 + X)) = 129600 ((12800 + 400X) + -100X * (32 + X)) = 129600 (12800 + 400X + (32 * -100X + X * -100X)) = 129600 (12800 + 400X + (-3200X + -100X2)) = 129600 Combine like terms: 400X + -3200X = -2800X (12800 + -2800X + -100X2) = 129600 Solving 12800 + -2800X + -100X2 = 129600 Solving for variable 'X'. Reorder the terms: 12800 + -129600 + -2800X + -100X2 = 129600 + -129600 Combine like terms: 12800 + -129600 = -116800 -116800 + -2800X + -100X2 = 129600 + -129600 Combine like terms: 129600 + -129600 = 0 -116800 + -2800X + -100X2 = 0 Factor out the Greatest Common Factor (GCF), '-100'. -100(1168 + 28X + X2) = 0 Ignore the factor -100.Subproblem 1
Set the factor '(1168 + 28X + X2)' equal to zero and attempt to solve: Simplifying 1168 + 28X + X2 = 0 Solving 1168 + 28X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-1168' to each side of the equation. 1168 + 28X + -1168 + X2 = 0 + -1168 Reorder the terms: 1168 + -1168 + 28X + X2 = 0 + -1168 Combine like terms: 1168 + -1168 = 0 0 + 28X + X2 = 0 + -1168 28X + X2 = 0 + -1168 Combine like terms: 0 + -1168 = -1168 28X + X2 = -1168 The X term is 28X. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28X + 196 + X2 = -1168 + 196 Reorder the terms: 196 + 28X + X2 = -1168 + 196 Combine like terms: -1168 + 196 = -972 196 + 28X + X2 = -972 Factor a perfect square on the left side: (X + 14)(X + 14) = -972 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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