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Simplifying 5x2 + x + -384 = 0 Reorder the terms: -384 + x + 5x2 = 0 Solving -384 + x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -76.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '76.8' to each side of the equation. -76.8 + 0.2x + 76.8 + x2 = 0 + 76.8 Reorder the terms: -76.8 + 76.8 + 0.2x + x2 = 0 + 76.8 Combine like terms: -76.8 + 76.8 = 0.0 0.0 + 0.2x + x2 = 0 + 76.8 0.2x + x2 = 0 + 76.8 Combine like terms: 0 + 76.8 = 76.8 0.2x + x2 = 76.8 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. 0.2x + 0.25 + x2 = 76.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 76.8 + 0.25 Combine like terms: 76.8 + 0.25 = 77.05 0.25 + 0.2x + x2 = 77.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 77.05 Calculate the square root of the right side: 8.777812939 Break this problem into two subproblems by setting (x + 0.5) equal to 8.777812939 and -8.777812939.Subproblem 1
x + 0.5 = 8.777812939 Simplifying x + 0.5 = 8.777812939 Reorder the terms: 0.5 + x = 8.777812939 Solving 0.5 + x = 8.777812939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.777812939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.777812939 + -0.5 x = 8.777812939 + -0.5 Combine like terms: 8.777812939 + -0.5 = 8.277812939 x = 8.277812939 Simplifying x = 8.277812939Subproblem 2
x + 0.5 = -8.777812939 Simplifying x + 0.5 = -8.777812939 Reorder the terms: 0.5 + x = -8.777812939 Solving 0.5 + x = -8.777812939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.777812939 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.777812939 + -0.5 x = -8.777812939 + -0.5 Combine like terms: -8.777812939 + -0.5 = -9.277812939 x = -9.277812939 Simplifying x = -9.277812939Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.277812939, -9.277812939}
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