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Simplifying 20x(20 + -1x) + 100 = 3500 (20 * 20x + -1x * 20x) + 100 = 3500 (400x + -20x2) + 100 = 3500 Reorder the terms: 100 + 400x + -20x2 = 3500 Solving 100 + 400x + -20x2 = 3500 Solving for variable 'x'. Reorder the terms: 100 + -3500 + 400x + -20x2 = 3500 + -3500 Combine like terms: 100 + -3500 = -3400 -3400 + 400x + -20x2 = 3500 + -3500 Combine like terms: 3500 + -3500 = 0 -3400 + 400x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-170 + 20x + -1x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-170 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -170 + 20x + -1x2 = 0 Solving -170 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 170 + -20x + x2 = 0 Move the constant term to the right: Add '-170' to each side of the equation. 170 + -20x + -170 + x2 = 0 + -170 Reorder the terms: 170 + -170 + -20x + x2 = 0 + -170 Combine like terms: 170 + -170 = 0 0 + -20x + x2 = 0 + -170 -20x + x2 = 0 + -170 Combine like terms: 0 + -170 = -170 -20x + x2 = -170 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -170 + 100 Reorder the terms: 100 + -20x + x2 = -170 + 100 Combine like terms: -170 + 100 = -70 100 + -20x + x2 = -70 Factor a perfect square on the left side: (x + -10)(x + -10) = -70 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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