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Simplifying 4x(x + 3) + -1(x + -5) * 10 = 4 Reorder the terms: 4x(3 + x) + -1(x + -5) * 10 = 4 (3 * 4x + x * 4x) + -1(x + -5) * 10 = 4 (12x + 4x2) + -1(x + -5) * 10 = 4 Reorder the terms: 12x + 4x2 + -1(-5 + x) * 10 = 4 Reorder the terms for easier multiplication: 12x + 4x2 + -1 * 10(-5 + x) = 4 Multiply -1 * 10 12x + 4x2 + -10(-5 + x) = 4 12x + 4x2 + (-5 * -10 + x * -10) = 4 12x + 4x2 + (50 + -10x) = 4 Reorder the terms: 50 + 12x + -10x + 4x2 = 4 Combine like terms: 12x + -10x = 2x 50 + 2x + 4x2 = 4 Solving 50 + 2x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: 50 + -4 + 2x + 4x2 = 4 + -4 Combine like terms: 50 + -4 = 46 46 + 2x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 46 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(23 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + x + 2x2)' equal to zero and attempt to solve: Simplifying 23 + x + 2x2 = 0 Solving 23 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + 0.5x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + 0.5x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + 0.5x + x2 = 0 + -11.5 0.5x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 0.5x + x2 = -11.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = -11.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -11.5 + 0.25 Combine like terms: -11.5 + 0.25 = -11.25 0.25 + 0.5x + x2 = -11.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -11.25 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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