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Simplifying r2 + 576 = 2r2 + 32r + 1024 Reorder the terms: 576 + r2 = 2r2 + 32r + 1024 Reorder the terms: 576 + r2 = 1024 + 32r + 2r2 Solving 576 + r2 = 1024 + 32r + 2r2 Solving for variable 'r'. Reorder the terms: 576 + -1024 + -32r + r2 + -2r2 = 1024 + 32r + 2r2 + -1024 + -32r + -2r2 Combine like terms: 576 + -1024 = -448 -448 + -32r + r2 + -2r2 = 1024 + 32r + 2r2 + -1024 + -32r + -2r2 Combine like terms: r2 + -2r2 = -1r2 -448 + -32r + -1r2 = 1024 + 32r + 2r2 + -1024 + -32r + -2r2 Reorder the terms: -448 + -32r + -1r2 = 1024 + -1024 + 32r + -32r + 2r2 + -2r2 Combine like terms: 1024 + -1024 = 0 -448 + -32r + -1r2 = 0 + 32r + -32r + 2r2 + -2r2 -448 + -32r + -1r2 = 32r + -32r + 2r2 + -2r2 Combine like terms: 32r + -32r = 0 -448 + -32r + -1r2 = 0 + 2r2 + -2r2 -448 + -32r + -1r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -448 + -32r + -1r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(448 + 32r + r2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(448 + 32r + r2)' equal to zero and attempt to solve: Simplifying 448 + 32r + r2 = 0 Solving 448 + 32r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-448' to each side of the equation. 448 + 32r + -448 + r2 = 0 + -448 Reorder the terms: 448 + -448 + 32r + r2 = 0 + -448 Combine like terms: 448 + -448 = 0 0 + 32r + r2 = 0 + -448 32r + r2 = 0 + -448 Combine like terms: 0 + -448 = -448 32r + r2 = -448 The r term is 32r. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32r + 256 + r2 = -448 + 256 Reorder the terms: 256 + 32r + r2 = -448 + 256 Combine like terms: -448 + 256 = -192 256 + 32r + r2 = -192 Factor a perfect square on the left side: (r + 16)(r + 16) = -192 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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