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Simplifying x2 + -20x = 6x2 + -2x + 20 Reorder the terms: -20x + x2 = 6x2 + -2x + 20 Reorder the terms: -20x + x2 = 20 + -2x + 6x2 Solving -20x + x2 = 20 + -2x + 6x2 Solving for variable 'x'. Reorder the terms: -20 + -20x + 2x + x2 + -6x2 = 20 + -2x + 6x2 + -20 + 2x + -6x2 Combine like terms: -20x + 2x = -18x -20 + -18x + x2 + -6x2 = 20 + -2x + 6x2 + -20 + 2x + -6x2 Combine like terms: x2 + -6x2 = -5x2 -20 + -18x + -5x2 = 20 + -2x + 6x2 + -20 + 2x + -6x2 Reorder the terms: -20 + -18x + -5x2 = 20 + -20 + -2x + 2x + 6x2 + -6x2 Combine like terms: 20 + -20 = 0 -20 + -18x + -5x2 = 0 + -2x + 2x + 6x2 + -6x2 -20 + -18x + -5x2 = -2x + 2x + 6x2 + -6x2 Combine like terms: -2x + 2x = 0 -20 + -18x + -5x2 = 0 + 6x2 + -6x2 -20 + -18x + -5x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -20 + -18x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 18x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 18x + 5x2)' equal to zero and attempt to solve: Simplifying 20 + 18x + 5x2 = 0 Solving 20 + 18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + 3.6x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 3.6x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 3.6x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3.6x + x2 = 0 + -4 3.6x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 3.6x + x2 = -4 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -4 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -4 + 3.24 Combine like terms: -4 + 3.24 = -0.76 3.24 + 3.6x + x2 = -0.76 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = -0.76 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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