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Simplifying 80x = 2x2 + 1700 Reorder the terms: 80x = 1700 + 2x2 Solving 80x = 1700 + 2x2 Solving for variable 'x'. Reorder the terms: -1700 + 80x + -2x2 = 1700 + 2x2 + -1700 + -2x2 Reorder the terms: -1700 + 80x + -2x2 = 1700 + -1700 + 2x2 + -2x2 Combine like terms: 1700 + -1700 = 0 -1700 + 80x + -2x2 = 0 + 2x2 + -2x2 -1700 + 80x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1700 + 80x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-850 + 40x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-850 + 40x + -1x2)' equal to zero and attempt to solve: Simplifying -850 + 40x + -1x2 = 0 Solving -850 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 850 + -40x + x2 = 0 Move the constant term to the right: Add '-850' to each side of the equation. 850 + -40x + -850 + x2 = 0 + -850 Reorder the terms: 850 + -850 + -40x + x2 = 0 + -850 Combine like terms: 850 + -850 = 0 0 + -40x + x2 = 0 + -850 -40x + x2 = 0 + -850 Combine like terms: 0 + -850 = -850 -40x + x2 = -850 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -850 + 400 Reorder the terms: 400 + -40x + x2 = -850 + 400 Combine like terms: -850 + 400 = -450 400 + -40x + x2 = -450 Factor a perfect square on the left side: (x + -20)(x + -20) = -450 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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