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Simplifying 245x + -49(x * x) = 1960 Multiply x * x 245x + -49(x2) = 1960 Solving 245x + -49x2 = 1960 Solving for variable 'x'. Reorder the terms: -1960 + 245x + -49x2 = 1960 + -1960 Combine like terms: 1960 + -1960 = 0 -1960 + 245x + -49x2 = 0 Factor out the Greatest Common Factor (GCF), '49'. 49(-40 + 5x + -1x2) = 0 Ignore the factor 49.Subproblem 1
Set the factor '(-40 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -40 + 5x + -1x2 = 0 Solving -40 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 40 + -5x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -5x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -5x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -5x + x2 = 0 + -40 -5x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -5x + x2 = -40 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -40 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -40 + 6.25 Combine like terms: -40 + 6.25 = -33.75 6.25 + -5x + x2 = -33.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -33.75 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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