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Simplifying 25x2 + 80x + 54 = 0 Reorder the terms: 54 + 80x + 25x2 = 0 Solving 54 + 80x + 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 + 3.2x + x2 = 0 Move the constant term to the right: Add '-2.16' to each side of the equation. 2.16 + 3.2x + -2.16 + x2 = 0 + -2.16 Reorder the terms: 2.16 + -2.16 + 3.2x + x2 = 0 + -2.16 Combine like terms: 2.16 + -2.16 = 0.00 0.00 + 3.2x + x2 = 0 + -2.16 3.2x + x2 = 0 + -2.16 Combine like terms: 0 + -2.16 = -2.16 3.2x + x2 = -2.16 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -2.16 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -2.16 + 2.56 Combine like terms: -2.16 + 2.56 = 0.4 2.56 + 3.2x + x2 = 0.4 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + 1.6) equal to 0.632455532 and -0.632455532.Subproblem 1
x + 1.6 = 0.632455532 Simplifying x + 1.6 = 0.632455532 Reorder the terms: 1.6 + x = 0.632455532 Solving 1.6 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 0.632455532 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 0.632455532 + -1.6 x = 0.632455532 + -1.6 Combine like terms: 0.632455532 + -1.6 = -0.967544468 x = -0.967544468 Simplifying x = -0.967544468Subproblem 2
x + 1.6 = -0.632455532 Simplifying x + 1.6 = -0.632455532 Reorder the terms: 1.6 + x = -0.632455532 Solving 1.6 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -0.632455532 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -0.632455532 + -1.6 x = -0.632455532 + -1.6 Combine like terms: -0.632455532 + -1.6 = -2.232455532 x = -2.232455532 Simplifying x = -2.232455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.967544468, -2.232455532}
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