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Simplifying (50x)(50x) + 200x + 150 = 0 Remove parenthesis around (50x) 50x(50x) + 200x + 150 = 0 Remove parenthesis around (50x) 50x * 50x + 200x + 150 = 0 Reorder the terms for easier multiplication: 50 * 50x * x + 200x + 150 = 0 Multiply 50 * 50 2500x * x + 200x + 150 = 0 Multiply x * x 2500x2 + 200x + 150 = 0 Reorder the terms: 150 + 200x + 2500x2 = 0 Solving 150 + 200x + 2500x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(3 + 4x + 50x2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(3 + 4x + 50x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 50x2 = 0 Solving 3 + 4x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.06 + 0.08x + x2 = 0.0 Move the constant term to the right: Add '-0.06' to each side of the equation. 0.06 + 0.08x + -0.06 + x2 = 0.0 + -0.06 Reorder the terms: 0.06 + -0.06 + 0.08x + x2 = 0.0 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + 0.08x + x2 = 0.0 + -0.06 0.08x + x2 = 0.0 + -0.06 Combine like terms: 0.0 + -0.06 = -0.06 0.08x + x2 = -0.06 The x term is 0.08x. Take half its coefficient (0.04). Square it (0.0016) and add it to both sides. Add '0.0016' to each side of the equation. 0.08x + 0.0016 + x2 = -0.06 + 0.0016 Reorder the terms: 0.0016 + 0.08x + x2 = -0.06 + 0.0016 Combine like terms: -0.06 + 0.0016 = -0.0584 0.0016 + 0.08x + x2 = -0.0584 Factor a perfect square on the left side: (x + 0.04)(x + 0.04) = -0.0584 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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