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Simplifying (-4x2 + 2x + -4) + -1(6x2 + 5x) = 0 Reorder the terms: (-4 + 2x + -4x2) + -1(6x2 + 5x) = 0 Remove parenthesis around (-4 + 2x + -4x2) -4 + 2x + -4x2 + -1(6x2 + 5x) = 0 Reorder the terms: -4 + 2x + -4x2 + -1(5x + 6x2) = 0 -4 + 2x + -4x2 + (5x * -1 + 6x2 * -1) = 0 -4 + 2x + -4x2 + (-5x + -6x2) = 0 Reorder the terms: -4 + 2x + -5x + -4x2 + -6x2 = 0 Combine like terms: 2x + -5x = -3x -4 + -3x + -4x2 + -6x2 = 0 Combine like terms: -4x2 + -6x2 = -10x2 -4 + -3x + -10x2 = 0 Solving -4 + -3x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 3x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 3x + 10x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 10x2 = 0 Solving 4 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.3x + -0.4 + x2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.3x + x2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.3x + x2 = 0.0 + -0.4 0.3x + x2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 0.3x + x2 = -0.4 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = -0.4 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = -0.4 + 0.0225 Combine like terms: -0.4 + 0.0225 = -0.3775 0.0225 + 0.3x + x2 = -0.3775 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = -0.3775 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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