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Simplifying x + -5 + 4x = 4x(x + 3) Reorder the terms: -5 + x + 4x = 4x(x + 3) Combine like terms: x + 4x = 5x -5 + 5x = 4x(x + 3) Reorder the terms: -5 + 5x = 4x(3 + x) -5 + 5x = (3 * 4x + x * 4x) -5 + 5x = (12x + 4x2) Solving -5 + 5x = 12x + 4x2 Solving for variable 'x'. Combine like terms: 5x + -12x = -7x -5 + -7x + -4x2 = 12x + 4x2 + -12x + -4x2 Reorder the terms: -5 + -7x + -4x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -5 + -7x + -4x2 = 0 + 4x2 + -4x2 -5 + -7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -5 + -7x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 7x + 4x2) = 0 Ignore the factor -1.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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