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Simplifying 5 + -4x(7 + 2x) = 50 + -2x 5 + (7 * -4x + 2x * -4x) = 50 + -2x 5 + (-28x + -8x2) = 50 + -2x Solving 5 + -28x + -8x2 = 50 + -2x Solving for variable 'x'. Reorder the terms: 5 + -50 + -28x + 2x + -8x2 = 50 + -2x + -50 + 2x Combine like terms: 5 + -50 = -45 -45 + -28x + 2x + -8x2 = 50 + -2x + -50 + 2x Combine like terms: -28x + 2x = -26x -45 + -26x + -8x2 = 50 + -2x + -50 + 2x Reorder the terms: -45 + -26x + -8x2 = 50 + -50 + -2x + 2x Combine like terms: 50 + -50 = 0 -45 + -26x + -8x2 = 0 + -2x + 2x -45 + -26x + -8x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -45 + -26x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 26x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 26x + 8x2)' equal to zero and attempt to solve: Simplifying 45 + 26x + 8x2 = 0 Solving 45 + 26x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.625 + 3.25x + x2 = 0 Move the constant term to the right: Add '-5.625' to each side of the equation. 5.625 + 3.25x + -5.625 + x2 = 0 + -5.625 Reorder the terms: 5.625 + -5.625 + 3.25x + x2 = 0 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + 3.25x + x2 = 0 + -5.625 3.25x + x2 = 0 + -5.625 Combine like terms: 0 + -5.625 = -5.625 3.25x + x2 = -5.625 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -5.625 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -5.625 + 2.640625 Combine like terms: -5.625 + 2.640625 = -2.984375 2.640625 + 3.25x + x2 = -2.984375 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = -2.984375 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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