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Simplifying 2(4x2 + 5x + 2) + 2(x + 7) = 0 Reorder the terms: 2(2 + 5x + 4x2) + 2(x + 7) = 0 (2 * 2 + 5x * 2 + 4x2 * 2) + 2(x + 7) = 0 (4 + 10x + 8x2) + 2(x + 7) = 0 Reorder the terms: 4 + 10x + 8x2 + 2(7 + x) = 0 4 + 10x + 8x2 + (7 * 2 + x * 2) = 0 4 + 10x + 8x2 + (14 + 2x) = 0 Reorder the terms: 4 + 14 + 10x + 2x + 8x2 = 0 Combine like terms: 4 + 14 = 18 18 + 10x + 2x + 8x2 = 0 Combine like terms: 10x + 2x = 12x 18 + 12x + 8x2 = 0 Solving 18 + 12x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 6x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 6x + 4x2 = 0 Solving 9 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 1.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 1.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 1.5x + x2 = 0 + -2.25 1.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 1.5x + x2 = -2.25 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 = -2.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2.25 + 0.5625 Combine like terms: -2.25 + 0.5625 = -1.6875 0.5625 + 1.5x + x2 = -1.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.6875 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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