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Simplifying 25x2 + -10x + -54 = 0 Reorder the terms: -54 + -10x + 25x2 = 0 Solving -54 + -10x + 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 + -0.4x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + -0.4x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + -0.4x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + -0.4x + x2 = 0 + 2.16 -0.4x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 -0.4x + x2 = 2.16 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 2.16 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 2.16 + 0.04 Combine like terms: 2.16 + 0.04 = 2.2 0.04 + -0.4x + x2 = 2.2 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (x + -0.2) equal to 1.483239697 and -1.483239697.Subproblem 1
x + -0.2 = 1.483239697 Simplifying x + -0.2 = 1.483239697 Reorder the terms: -0.2 + x = 1.483239697 Solving -0.2 + x = 1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.483239697 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.483239697 + 0.2 x = 1.483239697 + 0.2 Combine like terms: 1.483239697 + 0.2 = 1.683239697 x = 1.683239697 Simplifying x = 1.683239697Subproblem 2
x + -0.2 = -1.483239697 Simplifying x + -0.2 = -1.483239697 Reorder the terms: -0.2 + x = -1.483239697 Solving -0.2 + x = -1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.483239697 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.483239697 + 0.2 x = -1.483239697 + 0.2 Combine like terms: -1.483239697 + 0.2 = -1.283239697 x = -1.283239697 Simplifying x = -1.283239697Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.683239697, -1.283239697}
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