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Simplifying 5x2 + 8x + -44 = 0 Reorder the terms: -44 + 8x + 5x2 = 0 Solving -44 + 8x + 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'. -8.8 + 1.6x + x2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + 1.6x + 8.8 + x2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + 1.6x + x2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + 1.6x + x2 = 0 + 8.8 1.6x + x2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 1.6x + x2 = 8.8 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 8.8 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 8.8 + 0.64 Combine like terms: 8.8 + 0.64 = 9.44 0.64 + 1.6x + x2 = 9.44 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 9.44 Calculate the square root of the right side: 3.072458299 Break this problem into two subproblems by setting (x + 0.8) equal to 3.072458299 and -3.072458299.Subproblem 1
x + 0.8 = 3.072458299 Simplifying x + 0.8 = 3.072458299 Reorder the terms: 0.8 + x = 3.072458299 Solving 0.8 + x = 3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 3.072458299 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 3.072458299 + -0.8 x = 3.072458299 + -0.8 Combine like terms: 3.072458299 + -0.8 = 2.272458299 x = 2.272458299 Simplifying x = 2.272458299Subproblem 2
x + 0.8 = -3.072458299 Simplifying x + 0.8 = -3.072458299 Reorder the terms: 0.8 + x = -3.072458299 Solving 0.8 + x = -3.072458299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -3.072458299 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -3.072458299 + -0.8 x = -3.072458299 + -0.8 Combine like terms: -3.072458299 + -0.8 = -3.872458299 x = -3.872458299 Simplifying x = -3.872458299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.272458299, -3.872458299}
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