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Simplifying 4x2 + -3x + 12 + -2x2 + 7x + 16 = 0 Reorder the terms: 12 + 16 + -3x + 7x + 4x2 + -2x2 = 0 Combine like terms: 12 + 16 = 28 28 + -3x + 7x + 4x2 + -2x2 = 0 Combine like terms: -3x + 7x = 4x 28 + 4x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 28 + 4x + 2x2 = 0 Solving 28 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 2x + x2)' equal to zero and attempt to solve: Simplifying 14 + 2x + x2 = 0 Solving 14 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 2x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 2x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 2x + x2 = 0 + -14 2x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 2x + x2 = -14 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 = -14 + 1 Reorder the terms: 1 + 2x + x2 = -14 + 1 Combine like terms: -14 + 1 = -13 1 + 2x + x2 = -13 Factor a perfect square on the left side: (x + 1)(x + 1) = -13 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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