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Simplifying 0.4x2 + 4.4x = -4 Reorder the terms: 4.4x + 0.4x2 = -4 Solving 4.4x + 0.4x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 4.4x + 0.4x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 4.4x + 0.4x2 = 0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 10 + 11x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 11x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 11x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 11x + x2 = 0 + -10 11x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 11x + x2 = -10 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -10 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -10 + 30.25 Combine like terms: -10 + 30.25 = 20.25 30.25 + 11x + x2 = 20.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 20.25 Calculate the square root of the right side: 4.5 Break this problem into two subproblems by setting (x + 5.5) equal to 4.5 and -4.5.Subproblem 1
x + 5.5 = 4.5 Simplifying x + 5.5 = 4.5 Reorder the terms: 5.5 + x = 4.5 Solving 5.5 + x = 4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 4.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.5 + -5.5 x = 4.5 + -5.5 Combine like terms: 4.5 + -5.5 = -1 x = -1 Simplifying x = -1Subproblem 2
x + 5.5 = -4.5 Simplifying x + 5.5 = -4.5 Reorder the terms: 5.5 + x = -4.5 Solving 5.5 + x = -4.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -4.5 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.5 + -5.5 x = -4.5 + -5.5 Combine like terms: -4.5 + -5.5 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1, -10}
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