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Simplifying 2x(x + -3) + 9 = 4x + -7 Reorder the terms: 2x(-3 + x) + 9 = 4x + -7 (-3 * 2x + x * 2x) + 9 = 4x + -7 (-6x + 2x2) + 9 = 4x + -7 Reorder the terms: 9 + -6x + 2x2 = 4x + -7 Reorder the terms: 9 + -6x + 2x2 = -7 + 4x Solving 9 + -6x + 2x2 = -7 + 4x Solving for variable 'x'. Reorder the terms: 9 + 7 + -6x + -4x + 2x2 = -7 + 4x + 7 + -4x Combine like terms: 9 + 7 = 16 16 + -6x + -4x + 2x2 = -7 + 4x + 7 + -4x Combine like terms: -6x + -4x = -10x 16 + -10x + 2x2 = -7 + 4x + 7 + -4x Reorder the terms: 16 + -10x + 2x2 = -7 + 7 + 4x + -4x Combine like terms: -7 + 7 = 0 16 + -10x + 2x2 = 0 + 4x + -4x 16 + -10x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 16 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -5x + x2)' equal to zero and attempt to solve: Simplifying 8 + -5x + x2 = 0 Solving 8 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x + x2 = 0 + -8 -5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5x + x2 = -8 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -8 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -8 + 6.25 Combine like terms: -8 + 6.25 = -1.75 6.25 + -5x + x2 = -1.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -1.75 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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