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Simplifying 2(x2 + 14x + 85) = 0 Reorder the terms: 2(85 + 14x + x2) = 0 (85 * 2 + 14x * 2 + x2 * 2) = 0 (170 + 28x + 2x2) = 0 Solving 170 + 28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(85 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(85 + 14x + x2)' equal to zero and attempt to solve: Simplifying 85 + 14x + x2 = 0 Solving 85 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-85' to each side of the equation. 85 + 14x + -85 + x2 = 0 + -85 Reorder the terms: 85 + -85 + 14x + x2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + 14x + x2 = 0 + -85 14x + x2 = 0 + -85 Combine like terms: 0 + -85 = -85 14x + x2 = -85 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 = -85 + 49 Reorder the terms: 49 + 14x + x2 = -85 + 49 Combine like terms: -85 + 49 = -36 49 + 14x + x2 = -36 Factor a perfect square on the left side: (x + 7)(x + 7) = -36 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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