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Simplifying 3x2 + 4x = 7x2 + 6x + 1 Reorder the terms: 4x + 3x2 = 7x2 + 6x + 1 Reorder the terms: 4x + 3x2 = 1 + 6x + 7x2 Solving 4x + 3x2 = 1 + 6x + 7x2 Solving for variable 'x'. Reorder the terms: -1 + 4x + -6x + 3x2 + -7x2 = 1 + 6x + 7x2 + -1 + -6x + -7x2 Combine like terms: 4x + -6x = -2x -1 + -2x + 3x2 + -7x2 = 1 + 6x + 7x2 + -1 + -6x + -7x2 Combine like terms: 3x2 + -7x2 = -4x2 -1 + -2x + -4x2 = 1 + 6x + 7x2 + -1 + -6x + -7x2 Reorder the terms: -1 + -2x + -4x2 = 1 + -1 + 6x + -6x + 7x2 + -7x2 Combine like terms: 1 + -1 = 0 -1 + -2x + -4x2 = 0 + 6x + -6x + 7x2 + -7x2 -1 + -2x + -4x2 = 6x + -6x + 7x2 + -7x2 Combine like terms: 6x + -6x = 0 -1 + -2x + -4x2 = 0 + 7x2 + -7x2 -1 + -2x + -4x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -1 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 2x + 4x2) = 0 Ignore the factor -1.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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