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Simplifying 25x2 + 90x + 44 = 0 Reorder the terms: 44 + 90x + 25x2 = 0 Solving 44 + 90x + 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'. 1.76 + 3.6x + x2 = 0 Move the constant term to the right: Add '-1.76' to each side of the equation. 1.76 + 3.6x + -1.76 + x2 = 0 + -1.76 Reorder the terms: 1.76 + -1.76 + 3.6x + x2 = 0 + -1.76 Combine like terms: 1.76 + -1.76 = 0.00 0.00 + 3.6x + x2 = 0 + -1.76 3.6x + x2 = 0 + -1.76 Combine like terms: 0 + -1.76 = -1.76 3.6x + x2 = -1.76 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = -1.76 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = -1.76 + 3.24 Combine like terms: -1.76 + 3.24 = 1.48 3.24 + 3.6x + x2 = 1.48 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 1.48 Calculate the square root of the right side: 1.216552506 Break this problem into two subproblems by setting (x + 1.8) equal to 1.216552506 and -1.216552506.Subproblem 1
x + 1.8 = 1.216552506 Simplifying x + 1.8 = 1.216552506 Reorder the terms: 1.8 + x = 1.216552506 Solving 1.8 + x = 1.216552506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 1.216552506 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 1.216552506 + -1.8 x = 1.216552506 + -1.8 Combine like terms: 1.216552506 + -1.8 = -0.583447494 x = -0.583447494 Simplifying x = -0.583447494Subproblem 2
x + 1.8 = -1.216552506 Simplifying x + 1.8 = -1.216552506 Reorder the terms: 1.8 + x = -1.216552506 Solving 1.8 + x = -1.216552506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -1.216552506 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -1.216552506 + -1.8 x = -1.216552506 + -1.8 Combine like terms: -1.216552506 + -1.8 = -3.016552506 x = -3.016552506 Simplifying x = -3.016552506Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.583447494, -3.016552506}
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