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Simplifying x2 + -49 = 4x2 + 24x + 36 Reorder the terms: -49 + x2 = 4x2 + 24x + 36 Reorder the terms: -49 + x2 = 36 + 24x + 4x2 Solving -49 + x2 = 36 + 24x + 4x2 Solving for variable 'x'. Reorder the terms: -49 + -36 + -24x + x2 + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: -49 + -36 = -85 -85 + -24x + x2 + -4x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Combine like terms: x2 + -4x2 = -3x2 -85 + -24x + -3x2 = 36 + 24x + 4x2 + -36 + -24x + -4x2 Reorder the terms: -85 + -24x + -3x2 = 36 + -36 + 24x + -24x + 4x2 + -4x2 Combine like terms: 36 + -36 = 0 -85 + -24x + -3x2 = 0 + 24x + -24x + 4x2 + -4x2 -85 + -24x + -3x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 -85 + -24x + -3x2 = 0 + 4x2 + -4x2 -85 + -24x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -85 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(85 + 24x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(85 + 24x + 3x2)' equal to zero and attempt to solve: Simplifying 85 + 24x + 3x2 = 0 Solving 85 + 24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 28.33333333 + 8x + x2 = 0 Move the constant term to the right: Add '-28.33333333' to each side of the equation. 28.33333333 + 8x + -28.33333333 + x2 = 0 + -28.33333333 Reorder the terms: 28.33333333 + -28.33333333 + 8x + x2 = 0 + -28.33333333 Combine like terms: 28.33333333 + -28.33333333 = 0.00000000 0.00000000 + 8x + x2 = 0 + -28.33333333 8x + x2 = 0 + -28.33333333 Combine like terms: 0 + -28.33333333 = -28.33333333 8x + x2 = -28.33333333 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 = -28.33333333 + 16 Reorder the terms: 16 + 8x + x2 = -28.33333333 + 16 Combine like terms: -28.33333333 + 16 = -12.33333333 16 + 8x + x2 = -12.33333333 Factor a perfect square on the left side: (x + 4)(x + 4) = -12.33333333 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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