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Simplifying x = x2 + 10x + 21 Reorder the terms: x = 21 + 10x + x2 Solving x = 21 + 10x + x2 Solving for variable 'x'. Reorder the terms: -21 + x + -10x + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2 Combine like terms: x + -10x = -9x -21 + -9x + -1x2 = 21 + 10x + x2 + -21 + -10x + -1x2 Reorder the terms: -21 + -9x + -1x2 = 21 + -21 + 10x + -10x + x2 + -1x2 Combine like terms: 21 + -21 = 0 -21 + -9x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -21 + -9x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -21 + -9x + -1x2 = 0 + x2 + -1x2 -21 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -21 + -9x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 9x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 9x + x2)' equal to zero and attempt to solve: Simplifying 21 + 9x + x2 = 0 Solving 21 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 9x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 9x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 9x + x2 = 0 + -21 9x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 9x + x2 = -21 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -21 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -21 + 20.25 Combine like terms: -21 + 20.25 = -0.75 20.25 + 9x + x2 = -0.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = -0.75 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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