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Simplifying 9((x2 + -1x) + -4) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Reorder the terms: 9((-1x + x2) + -4) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Remove parenthesis around (-1x + x2) 9(-1x + x2 + -4) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Reorder the terms: 9(-4 + -1x + x2) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) (-4 * 9 + -1x * 9 + x2 * 9) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) (-36 + -9x + 9x2) + 4 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Reorder the terms: -36 + 4 + -9x + 9x2 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Combine like terms: -36 + 4 = -32 -32 + -9x + 9x2 = 9(x2 + -1x) + -4(4 + -1(x2 + -1x)) Reorder the terms: -32 + -9x + 9x2 = 9(-1x + x2) + -4(4 + -1(x2 + -1x)) -32 + -9x + 9x2 = (-1x * 9 + x2 * 9) + -4(4 + -1(x2 + -1x)) -32 + -9x + 9x2 = (-9x + 9x2) + -4(4 + -1(x2 + -1x)) Reorder the terms: -32 + -9x + 9x2 = -9x + 9x2 + -4(4 + -1(-1x + x2)) -32 + -9x + 9x2 = -9x + 9x2 + -4(4 + (-1x * -1 + x2 * -1)) -32 + -9x + 9x2 = -9x + 9x2 + -4(4 + (1x + -1x2)) -32 + -9x + 9x2 = -9x + 9x2 + (4 * -4 + 1x * -4 + -1x2 * -4) -32 + -9x + 9x2 = -9x + 9x2 + (-16 + -4x + 4x2) Reorder the terms: -32 + -9x + 9x2 = -16 + -9x + -4x + 9x2 + 4x2 Combine like terms: -9x + -4x = -13x -32 + -9x + 9x2 = -16 + -13x + 9x2 + 4x2 Combine like terms: 9x2 + 4x2 = 13x2 -32 + -9x + 9x2 = -16 + -13x + 13x2 Solving -32 + -9x + 9x2 = -16 + -13x + 13x2 Solving for variable 'x'. Reorder the terms: -32 + 16 + -9x + 13x + 9x2 + -13x2 = -16 + -13x + 13x2 + 16 + 13x + -13x2 Combine like terms: -32 + 16 = -16 -16 + -9x + 13x + 9x2 + -13x2 = -16 + -13x + 13x2 + 16 + 13x + -13x2 Combine like terms: -9x + 13x = 4x -16 + 4x + 9x2 + -13x2 = -16 + -13x + 13x2 + 16 + 13x + -13x2 Combine like terms: 9x2 + -13x2 = -4x2 -16 + 4x + -4x2 = -16 + -13x + 13x2 + 16 + 13x + -13x2 Reorder the terms: -16 + 4x + -4x2 = -16 + 16 + -13x + 13x + 13x2 + -13x2 Combine like terms: -16 + 16 = 0 -16 + 4x + -4x2 = 0 + -13x + 13x + 13x2 + -13x2 -16 + 4x + -4x2 = -13x + 13x + 13x2 + -13x2 Combine like terms: -13x + 13x = 0 -16 + 4x + -4x2 = 0 + 13x2 + -13x2 -16 + 4x + -4x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 -16 + 4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + x + -1x2 = 0 Solving -4 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -1x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x + x2 = 0 + -4 -1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1x + x2 = -4 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 = -4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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