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Simplifying 6x2 + 84x + 270 = -36 Reorder the terms: 270 + 84x + 6x2 = -36 Solving 270 + 84x + 6x2 = -36 Solving for variable 'x'. Reorder the terms: 270 + 36 + 84x + 6x2 = -36 + 36 Combine like terms: 270 + 36 = 306 306 + 84x + 6x2 = -36 + 36 Combine like terms: -36 + 36 = 0 306 + 84x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(51 + 14x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(51 + 14x + x2)' equal to zero and attempt to solve: Simplifying 51 + 14x + x2 = 0 Solving 51 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + 14x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + 14x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 14x + x2 = 0 + -51 14x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 14x + x2 = -51 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -51 + 49 Reorder the terms: 49 + 14x + x2 = -51 + 49 Combine like terms: -51 + 49 = -2 49 + 14x + x2 = -2 Factor a perfect square on the left side: (x + 7)(x + 7) = -2 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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