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Simplifying 4x(2x + 3) + 2(x + 5) = 0 Reorder the terms: 4x(3 + 2x) + 2(x + 5) = 0 (3 * 4x + 2x * 4x) + 2(x + 5) = 0 (12x + 8x2) + 2(x + 5) = 0 Reorder the terms: 12x + 8x2 + 2(5 + x) = 0 12x + 8x2 + (5 * 2 + x * 2) = 0 12x + 8x2 + (10 + 2x) = 0 Reorder the terms: 10 + 12x + 2x + 8x2 = 0 Combine like terms: 12x + 2x = 14x 10 + 14x + 8x2 = 0 Solving 10 + 14x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 7x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + 4x2 = 0 Solving 5 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 1.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 1.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 1.75x + x2 = 0 + -1.25 1.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 1.75x + x2 = -1.25 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -1.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -1.25 + 0.765625 Combine like terms: -1.25 + 0.765625 = -0.484375 0.765625 + 1.75x + x2 = -0.484375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -0.484375 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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