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Simplifying 6x(x + 2) = -42 Reorder the terms: 6x(2 + x) = -42 (2 * 6x + x * 6x) = -42 (12x + 6x2) = -42 Solving 12x + 6x2 = -42 Solving for variable 'x'. Reorder the terms: 42 + 12x + 6x2 = -42 + 42 Combine like terms: -42 + 42 = 0 42 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(7 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(7 + 2x + x2)' equal to zero and attempt to solve: Simplifying 7 + 2x + x2 = 0 Solving 7 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 2x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 2x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x + x2 = 0 + -7 2x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 2x + x2 = -7 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -7 + 1 Reorder the terms: 1 + 2x + x2 = -7 + 1 Combine like terms: -7 + 1 = -6 1 + 2x + x2 = -6 Factor a perfect square on the left side: (x + 1)(x + 1) = -6 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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