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Simplifying (5x2 + -7x + -4) + (2x2 + -3x + 5) + -1(x2 + -4x + -5) = 0 Reorder the terms: (-4 + -7x + 5x2) + (2x2 + -3x + 5) + -1(x2 + -4x + -5) = 0 Remove parenthesis around (-4 + -7x + 5x2) -4 + -7x + 5x2 + (2x2 + -3x + 5) + -1(x2 + -4x + -5) = 0 Reorder the terms: -4 + -7x + 5x2 + (5 + -3x + 2x2) + -1(x2 + -4x + -5) = 0 Remove parenthesis around (5 + -3x + 2x2) -4 + -7x + 5x2 + 5 + -3x + 2x2 + -1(x2 + -4x + -5) = 0 Reorder the terms: -4 + -7x + 5x2 + 5 + -3x + 2x2 + -1(-5 + -4x + x2) = 0 -4 + -7x + 5x2 + 5 + -3x + 2x2 + (-5 * -1 + -4x * -1 + x2 * -1) = 0 -4 + -7x + 5x2 + 5 + -3x + 2x2 + (5 + 4x + -1x2) = 0 Reorder the terms: -4 + 5 + 5 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -4 + 5 = 1 1 + 5 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: 1 + 5 = 6 6 + -7x + -3x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -7x + -3x = -10x 6 + -10x + 4x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: -10x + 4x = -6x 6 + -6x + 5x2 + 2x2 + -1x2 = 0 Combine like terms: 5x2 + 2x2 = 7x2 6 + -6x + 7x2 + -1x2 = 0 Combine like terms: 7x2 + -1x2 = 6x2 6 + -6x + 6x2 = 0 Solving 6 + -6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -1x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -1x + x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + x2 = 0 Solving 1 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 The x term is -1x. 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 = -1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1x + x2 = -0.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -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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