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Simplifying 20 + 3(8x + -2) * 5x = 0 Reorder the terms: 20 + 3(-2 + 8x) * 5x = 0 Reorder the terms for easier multiplication: 20 + 3 * 5x(-2 + 8x) = 0 Multiply 3 * 5 20 + 15x(-2 + 8x) = 0 20 + (-2 * 15x + 8x * 15x) = 0 20 + (-30x + 120x2) = 0 Solving 20 + -30x + 120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(2 + -3x + 12x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(2 + -3x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + 12x2 = 0 Solving 2 + -3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -0.25x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.25x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -0.25x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + -0.1666666667 -0.25x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -0.25x + x2 = -0.1666666667 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -0.1666666667 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -0.1666666667 + 0.015625 Combine like terms: -0.1666666667 + 0.015625 = -0.1510416667 0.015625 + -0.25x + x2 = -0.1510416667 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = -0.1510416667 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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