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Simplifying 4x = 200 + 2x2 Solving 4x = 200 + 2x2 Solving for variable 'x'. Reorder the terms: -200 + 4x + -2x2 = 200 + 2x2 + -200 + -2x2 Reorder the terms: -200 + 4x + -2x2 = 200 + -200 + 2x2 + -2x2 Combine like terms: 200 + -200 = 0 -200 + 4x + -2x2 = 0 + 2x2 + -2x2 -200 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -200 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -100 + 2x + -1x2 = 0 Solving -100 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -2x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -2x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -2x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -2x + x2 = 0 + -100 -2x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -2x + x2 = -100 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 = -100 + 1 Reorder the terms: 1 + -2x + x2 = -100 + 1 Combine like terms: -100 + 1 = -99 1 + -2x + x2 = -99 Factor a perfect square on the left side: (x + -1)(x + -1) = -99 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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