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Simplifying 5x2 + -1x + -54 = 0 Reorder the terms: -54 + -1x + 5x2 = 0 Solving -54 + -1x + 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 -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 10.8 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 10.8 + 0.01 Combine like terms: 10.8 + 0.01 = 10.81 0.01 + -0.2x + x2 = 10.81 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 10.81 Calculate the square root of the right side: 3.287856445 Break this problem into two subproblems by setting (x + -0.1) equal to 3.287856445 and -3.287856445.Subproblem 1
x + -0.1 = 3.287856445 Simplifying x + -0.1 = 3.287856445 Reorder the terms: -0.1 + x = 3.287856445 Solving -0.1 + x = 3.287856445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 3.287856445 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 3.287856445 + 0.1 x = 3.287856445 + 0.1 Combine like terms: 3.287856445 + 0.1 = 3.387856445 x = 3.387856445 Simplifying x = 3.387856445Subproblem 2
x + -0.1 = -3.287856445 Simplifying x + -0.1 = -3.287856445 Reorder the terms: -0.1 + x = -3.287856445 Solving -0.1 + x = -3.287856445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -3.287856445 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -3.287856445 + 0.1 x = -3.287856445 + 0.1 Combine like terms: -3.287856445 + 0.1 = -3.187856445 x = -3.187856445 Simplifying x = -3.187856445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.387856445, -3.187856445}
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