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Simplifying 2x(4x + -3) = 8x + 2 + -18 Reorder the terms: 2x(-3 + 4x) = 8x + 2 + -18 (-3 * 2x + 4x * 2x) = 8x + 2 + -18 (-6x + 8x2) = 8x + 2 + -18 Reorder the terms: -6x + 8x2 = 2 + -18 + 8x Combine like terms: 2 + -18 = -16 -6x + 8x2 = -16 + 8x Solving -6x + 8x2 = -16 + 8x Solving for variable 'x'. Reorder the terms: 16 + -6x + -8x + 8x2 = -16 + 8x + 16 + -8x Combine like terms: -6x + -8x = -14x 16 + -14x + 8x2 = -16 + 8x + 16 + -8x Reorder the terms: 16 + -14x + 8x2 = -16 + 16 + 8x + -8x Combine like terms: -16 + 16 = 0 16 + -14x + 8x2 = 0 + 8x + -8x 16 + -14x + 8x2 = 8x + -8x Combine like terms: 8x + -8x = 0 16 + -14x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying 8 + -7x + 4x2 = 0 Solving 8 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -1.75x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.75x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1.75x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.75x + x2 = 0 + -2 -1.75x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.75x + x2 = -2 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = -2 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = -2 + 0.765625 Combine like terms: -2 + 0.765625 = -1.234375 0.765625 + -1.75x + x2 = -1.234375 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = -1.234375 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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