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Simplifying 14000 = 400 + 700x + -100x2 Solving 14000 = 400 + 700x + -100x2 Solving for variable 'x'. Combine like terms: 14000 + -400 = 13600 13600 + -700x + 100x2 = 400 + 700x + -100x2 + -400 + -700x + 100x2 Reorder the terms: 13600 + -700x + 100x2 = 400 + -400 + 700x + -700x + -100x2 + 100x2 Combine like terms: 400 + -400 = 0 13600 + -700x + 100x2 = 0 + 700x + -700x + -100x2 + 100x2 13600 + -700x + 100x2 = 700x + -700x + -100x2 + 100x2 Combine like terms: 700x + -700x = 0 13600 + -700x + 100x2 = 0 + -100x2 + 100x2 13600 + -700x + 100x2 = -100x2 + 100x2 Combine like terms: -100x2 + 100x2 = 0 13600 + -700x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(136 + -7x + x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(136 + -7x + x2)' equal to zero and attempt to solve: Simplifying 136 + -7x + x2 = 0 Solving 136 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-136' to each side of the equation. 136 + -7x + -136 + x2 = 0 + -136 Reorder the terms: 136 + -136 + -7x + x2 = 0 + -136 Combine like terms: 136 + -136 = 0 0 + -7x + x2 = 0 + -136 -7x + x2 = 0 + -136 Combine like terms: 0 + -136 = -136 -7x + x2 = -136 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -136 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -136 + 12.25 Combine like terms: -136 + 12.25 = -123.75 12.25 + -7x + x2 = -123.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -123.75 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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