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Simplifying 25x2 + 17x + -54 = 0 Reorder the terms: -54 + 17x + 25x2 = 0 Solving -54 + 17x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.16 + 0.68x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + 0.68x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + 0.68x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + 0.68x + x2 = 0 + 2.16 0.68x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 0.68x + x2 = 2.16 The x term is 0.68x. Take half its coefficient (0.34). Square it (0.1156) and add it to both sides. Add '0.1156' to each side of the equation. 0.68x + 0.1156 + x2 = 2.16 + 0.1156 Reorder the terms: 0.1156 + 0.68x + x2 = 2.16 + 0.1156 Combine like terms: 2.16 + 0.1156 = 2.2756 0.1156 + 0.68x + x2 = 2.2756 Factor a perfect square on the left side: (x + 0.34)(x + 0.34) = 2.2756 Calculate the square root of the right side: 1.508509198 Break this problem into two subproblems by setting (x + 0.34) equal to 1.508509198 and -1.508509198.Subproblem 1
x + 0.34 = 1.508509198 Simplifying x + 0.34 = 1.508509198 Reorder the terms: 0.34 + x = 1.508509198 Solving 0.34 + x = 1.508509198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34' to each side of the equation. 0.34 + -0.34 + x = 1.508509198 + -0.34 Combine like terms: 0.34 + -0.34 = 0.00 0.00 + x = 1.508509198 + -0.34 x = 1.508509198 + -0.34 Combine like terms: 1.508509198 + -0.34 = 1.168509198 x = 1.168509198 Simplifying x = 1.168509198Subproblem 2
x + 0.34 = -1.508509198 Simplifying x + 0.34 = -1.508509198 Reorder the terms: 0.34 + x = -1.508509198 Solving 0.34 + x = -1.508509198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34' to each side of the equation. 0.34 + -0.34 + x = -1.508509198 + -0.34 Combine like terms: 0.34 + -0.34 = 0.00 0.00 + x = -1.508509198 + -0.34 x = -1.508509198 + -0.34 Combine like terms: -1.508509198 + -0.34 = -1.848509198 x = -1.848509198 Simplifying x = -1.848509198Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.168509198, -1.848509198}
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