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Simplifying 5x2 + x + -54 = 0 Reorder the terms: -54 + x + 5x2 = 0 Solving -54 + 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'. -10.8 + 0.2x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 0.2x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 0.2x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 0.2x + x2 = 0 + 10.8 0.2x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 0.2x + x2 = 10.8 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 = 10.8 + 0.25 Reorder the terms: 0.25 + 0.2x + x2 = 10.8 + 0.25 Combine like terms: 10.8 + 0.25 = 11.05 0.25 + 0.2x + x2 = 11.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.05 Calculate the square root of the right side: 3.324154028 Break this problem into two subproblems by setting (x + 0.5) equal to 3.324154028 and -3.324154028.Subproblem 1
x + 0.5 = 3.324154028 Simplifying x + 0.5 = 3.324154028 Reorder the terms: 0.5 + x = 3.324154028 Solving 0.5 + x = 3.324154028 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 = 3.324154028 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.324154028 + -0.5 x = 3.324154028 + -0.5 Combine like terms: 3.324154028 + -0.5 = 2.824154028 x = 2.824154028 Simplifying x = 2.824154028Subproblem 2
x + 0.5 = -3.324154028 Simplifying x + 0.5 = -3.324154028 Reorder the terms: 0.5 + x = -3.324154028 Solving 0.5 + x = -3.324154028 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 = -3.324154028 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.324154028 + -0.5 x = -3.324154028 + -0.5 Combine like terms: -3.324154028 + -0.5 = -3.824154028 x = -3.824154028 Simplifying x = -3.824154028Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.824154028, -3.824154028}
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