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Simplifying x = x2 + 19x + 84 Reorder the terms: x = 84 + 19x + x2 Solving x = 84 + 19x + x2 Solving for variable 'x'. Reorder the terms: -84 + x + -19x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2 Combine like terms: x + -19x = -18x -84 + -18x + -1x2 = 84 + 19x + x2 + -84 + -19x + -1x2 Reorder the terms: -84 + -18x + -1x2 = 84 + -84 + 19x + -19x + x2 + -1x2 Combine like terms: 84 + -84 = 0 -84 + -18x + -1x2 = 0 + 19x + -19x + x2 + -1x2 -84 + -18x + -1x2 = 19x + -19x + x2 + -1x2 Combine like terms: 19x + -19x = 0 -84 + -18x + -1x2 = 0 + x2 + -1x2 -84 + -18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -84 + -18x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(84 + 18x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(84 + 18x + x2)' equal to zero and attempt to solve: Simplifying 84 + 18x + x2 = 0 Solving 84 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 18x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 18x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 18x + x2 = 0 + -84 18x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 18x + x2 = -84 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -84 + 81 Reorder the terms: 81 + 18x + x2 = -84 + 81 Combine like terms: -84 + 81 = -3 81 + 18x + x2 = -3 Factor a perfect square on the left side: (x + 9)(x + 9) = -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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