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Simplifying (3x2 + 2x + -1) + -1(x2 + -4x + -7) = 0 Reorder the terms: (-1 + 2x + 3x2) + -1(x2 + -4x + -7) = 0 Remove parenthesis around (-1 + 2x + 3x2) -1 + 2x + 3x2 + -1(x2 + -4x + -7) = 0 Reorder the terms: -1 + 2x + 3x2 + -1(-7 + -4x + x2) = 0 -1 + 2x + 3x2 + (-7 * -1 + -4x * -1 + x2 * -1) = 0 -1 + 2x + 3x2 + (7 + 4x + -1x2) = 0 Reorder the terms: -1 + 7 + 2x + 4x + 3x2 + -1x2 = 0 Combine like terms: -1 + 7 = 6 6 + 2x + 4x + 3x2 + -1x2 = 0 Combine like terms: 2x + 4x = 6x 6 + 6x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 6 + 6x + 2x2 = 0 Solving 6 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 3x + x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + x2 = 0 Solving 3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3x + x2 = 0 + -3 3x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3x + x2 = -3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3x + x2 = -0.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.75 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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