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Simplifying 4000 = -16x2 + 160x Reorder the terms: 4000 = 160x + -16x2 Solving 4000 = 160x + -16x2 Solving for variable 'x'. Reorder the terms: 4000 + -160x + 16x2 = 160x + -160x + -16x2 + 16x2 Combine like terms: 160x + -160x = 0 4000 + -160x + 16x2 = 0 + -16x2 + 16x2 4000 + -160x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 4000 + -160x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(250 + -10x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(250 + -10x + x2)' equal to zero and attempt to solve: Simplifying 250 + -10x + x2 = 0 Solving 250 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-250' to each side of the equation. 250 + -10x + -250 + x2 = 0 + -250 Reorder the terms: 250 + -250 + -10x + x2 = 0 + -250 Combine like terms: 250 + -250 = 0 0 + -10x + x2 = 0 + -250 -10x + x2 = 0 + -250 Combine like terms: 0 + -250 = -250 -10x + x2 = -250 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -250 + 25 Reorder the terms: 25 + -10x + x2 = -250 + 25 Combine like terms: -250 + 25 = -225 25 + -10x + x2 = -225 Factor a perfect square on the left side: (x + -5)(x + -5) = -225 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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