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Simplifying 3x2 + 6x + 52 = 7 Reorder the terms: 52 + 6x + 3x2 = 7 Solving 52 + 6x + 3x2 = 7 Solving for variable 'x'. Reorder the terms: 52 + -7 + 6x + 3x2 = 7 + -7 Combine like terms: 52 + -7 = 45 45 + 6x + 3x2 = 7 + -7 Combine like terms: 7 + -7 = 0 45 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + 2x + x2)' equal to zero and attempt to solve: Simplifying 15 + 2x + x2 = 0 Solving 15 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 2x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 2x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2x + x2 = 0 + -15 2x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 2x + x2 = -15 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 = -15 + 1 Reorder the terms: 1 + 2x + x2 = -15 + 1 Combine like terms: -15 + 1 = -14 1 + 2x + x2 = -14 Factor a perfect square on the left side: (x + 1)(x + 1) = -14 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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