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Simplifying -160 = 4x + -4x(-2x + 7) Reorder the terms: -160 = 4x + -4x(7 + -2x) -160 = 4x + (7 * -4x + -2x * -4x) -160 = 4x + (-28x + 8x2) Combine like terms: 4x + -28x = -24x -160 = -24x + 8x2 Solving -160 = -24x + 8x2 Solving for variable 'x'. Reorder the terms: -160 + 24x + -8x2 = -24x + 24x + 8x2 + -8x2 Combine like terms: -24x + 24x = 0 -160 + 24x + -8x2 = 0 + 8x2 + -8x2 -160 + 24x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -160 + 24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-20 + 3x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-20 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 3x + -1x2 = 0 Solving -20 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -3x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -3x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -3x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -3x + x2 = 0 + -20 -3x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -3x + x2 = -20 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -20 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -20 + 2.25 Combine like terms: -20 + 2.25 = -17.75 2.25 + -3x + x2 = -17.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -17.75 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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