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Simplifying (2x2 + 3x + 1) + -1(4x2 + x + 7) = 0 Reorder the terms: (1 + 3x + 2x2) + -1(4x2 + x + 7) = 0 Remove parenthesis around (1 + 3x + 2x2) 1 + 3x + 2x2 + -1(4x2 + x + 7) = 0 Reorder the terms: 1 + 3x + 2x2 + -1(7 + x + 4x2) = 0 1 + 3x + 2x2 + (7 * -1 + x * -1 + 4x2 * -1) = 0 1 + 3x + 2x2 + (-7 + -1x + -4x2) = 0 Reorder the terms: 1 + -7 + 3x + -1x + 2x2 + -4x2 = 0 Combine like terms: 1 + -7 = -6 -6 + 3x + -1x + 2x2 + -4x2 = 0 Combine like terms: 3x + -1x = 2x -6 + 2x + 2x2 + -4x2 = 0 Combine like terms: 2x2 + -4x2 = -2x2 -6 + 2x + -2x2 = 0 Solving -6 + 2x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + x + -1x2 = 0 Solving -3 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -1x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x + x2 = 0 + -3 -1x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x + x2 = -3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -3 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + -1x + x2 = -2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.75 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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