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Simplifying 4x2 + 24x + 36 + 576 = x2 Reorder the terms: 36 + 576 + 24x + 4x2 = x2 Combine like terms: 36 + 576 = 612 612 + 24x + 4x2 = x2 Solving 612 + 24x + 4x2 = x2 Solving for variable 'x'. Combine like terms: 4x2 + -1x2 = 3x2 612 + 24x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 612 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(204 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(204 + 8x + x2)' equal to zero and attempt to solve: Simplifying 204 + 8x + x2 = 0 Solving 204 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-204' to each side of the equation. 204 + 8x + -204 + x2 = 0 + -204 Reorder the terms: 204 + -204 + 8x + x2 = 0 + -204 Combine like terms: 204 + -204 = 0 0 + 8x + x2 = 0 + -204 8x + x2 = 0 + -204 Combine like terms: 0 + -204 = -204 8x + x2 = -204 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -204 + 16 Reorder the terms: 16 + 8x + x2 = -204 + 16 Combine like terms: -204 + 16 = -188 16 + 8x + x2 = -188 Factor a perfect square on the left side: (x + 4)(x + 4) = -188 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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