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Simplifying 4x(x + -1) + -7 = (4x + 9) + -32 Reorder the terms: 4x(-1 + x) + -7 = (4x + 9) + -32 (-1 * 4x + x * 4x) + -7 = (4x + 9) + -32 (-4x + 4x2) + -7 = (4x + 9) + -32 Reorder the terms: -7 + -4x + 4x2 = (4x + 9) + -32 Reorder the terms: -7 + -4x + 4x2 = (9 + 4x) + -32 Remove parenthesis around (9 + 4x) -7 + -4x + 4x2 = 9 + 4x + -32 Reorder the terms: -7 + -4x + 4x2 = 9 + -32 + 4x Combine like terms: 9 + -32 = -23 -7 + -4x + 4x2 = -23 + 4x Solving -7 + -4x + 4x2 = -23 + 4x Solving for variable 'x'. Reorder the terms: -7 + 23 + -4x + -4x + 4x2 = -23 + 4x + 23 + -4x Combine like terms: -7 + 23 = 16 16 + -4x + -4x + 4x2 = -23 + 4x + 23 + -4x Combine like terms: -4x + -4x = -8x 16 + -8x + 4x2 = -23 + 4x + 23 + -4x Reorder the terms: 16 + -8x + 4x2 = -23 + 23 + 4x + -4x Combine like terms: -23 + 23 = 0 16 + -8x + 4x2 = 0 + 4x + -4x 16 + -8x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 16 + -8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -2x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -2x + x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + x2 = 0 Solving 4 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -2x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -2x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -2x + x2 = 0 + -4 -2x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -2x + x2 = -4 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -4 + 1 Reorder the terms: 1 + -2x + x2 = -4 + 1 Combine like terms: -4 + 1 = -3 1 + -2x + x2 = -3 Factor a perfect square on the left side: (x + -1)(x + -1) = -3 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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