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Simplifying 4x(x + 2) + 11 + -4 = 2x + 3 Reorder the terms: 4x(2 + x) + 11 + -4 = 2x + 3 (2 * 4x + x * 4x) + 11 + -4 = 2x + 3 (8x + 4x2) + 11 + -4 = 2x + 3 Reorder the terms: 11 + -4 + 8x + 4x2 = 2x + 3 Combine like terms: 11 + -4 = 7 7 + 8x + 4x2 = 2x + 3 Reorder the terms: 7 + 8x + 4x2 = 3 + 2x Solving 7 + 8x + 4x2 = 3 + 2x Solving for variable 'x'. Reorder the terms: 7 + -3 + 8x + -2x + 4x2 = 3 + 2x + -3 + -2x Combine like terms: 7 + -3 = 4 4 + 8x + -2x + 4x2 = 3 + 2x + -3 + -2x Combine like terms: 8x + -2x = 6x 4 + 6x + 4x2 = 3 + 2x + -3 + -2x Reorder the terms: 4 + 6x + 4x2 = 3 + -3 + 2x + -2x Combine like terms: 3 + -3 = 0 4 + 6x + 4x2 = 0 + 2x + -2x 4 + 6x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 4 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + 2x2 = 0 Solving 2 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5x + x2 = 0 + -1 1.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5x + x2 = -1 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.4375 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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