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Simplifying 8x2 + -7x + 4 = -3x + 2 Reorder the terms: 4 + -7x + 8x2 = -3x + 2 Reorder the terms: 4 + -7x + 8x2 = 2 + -3x Solving 4 + -7x + 8x2 = 2 + -3x Solving for variable 'x'. Reorder the terms: 4 + -2 + -7x + 3x + 8x2 = 2 + -3x + -2 + 3x Combine like terms: 4 + -2 = 2 2 + -7x + 3x + 8x2 = 2 + -3x + -2 + 3x Combine like terms: -7x + 3x = -4x 2 + -4x + 8x2 = 2 + -3x + -2 + 3x Reorder the terms: 2 + -4x + 8x2 = 2 + -2 + -3x + 3x Combine like terms: 2 + -2 = 0 2 + -4x + 8x2 = 0 + -3x + 3x 2 + -4x + 8x2 = -3x + 3x Combine like terms: -3x + 3x = 0 2 + -4x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -2x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -2x + 4x2 = 0 Solving 1 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.5x + x2 = 0 + -0.25 -0.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.5x + x2 = -0.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -0.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.25 + 0.0625 Combine like terms: -0.25 + 0.0625 = -0.1875 0.0625 + -0.5x + x2 = -0.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.1875 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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