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Simplifying 5x2 + 41x + -54 = 0 Reorder the terms: -54 + 41x + 5x2 = 0 Solving -54 + 41x + 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 + 8.2x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 8.2x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 8.2x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 8.2x + x2 = 0 + 10.8 8.2x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 8.2x + x2 = 10.8 The x term is 8.2x. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2x + 16.81 + x2 = 10.8 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = 10.8 + 16.81 Combine like terms: 10.8 + 16.81 = 27.61 16.81 + 8.2x + x2 = 27.61 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 27.61 Calculate the square root of the right side: 5.254521862 Break this problem into two subproblems by setting (x + 4.1) equal to 5.254521862 and -5.254521862.Subproblem 1
x + 4.1 = 5.254521862 Simplifying x + 4.1 = 5.254521862 Reorder the terms: 4.1 + x = 5.254521862 Solving 4.1 + x = 5.254521862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = 5.254521862 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 5.254521862 + -4.1 x = 5.254521862 + -4.1 Combine like terms: 5.254521862 + -4.1 = 1.154521862 x = 1.154521862 Simplifying x = 1.154521862Subproblem 2
x + 4.1 = -5.254521862 Simplifying x + 4.1 = -5.254521862 Reorder the terms: 4.1 + x = -5.254521862 Solving 4.1 + x = -5.254521862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = -5.254521862 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -5.254521862 + -4.1 x = -5.254521862 + -4.1 Combine like terms: -5.254521862 + -4.1 = -9.354521862 x = -9.354521862 Simplifying x = -9.354521862Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.154521862, -9.354521862}
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