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Simplifying 5x2 + 32x + 24 = 0 Reorder the terms: 24 + 32x + 5x2 = 0 Solving 24 + 32x + 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'. 4.8 + 6.4x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 6.4x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 6.4x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 6.4x + x2 = 0 + -4.8 6.4x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 6.4x + x2 = -4.8 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = -4.8 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = -4.8 + 10.24 Combine like terms: -4.8 + 10.24 = 5.44 10.24 + 6.4x + x2 = 5.44 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (x + 3.2) equal to 2.332380758 and -2.332380758.Subproblem 1
x + 3.2 = 2.332380758 Simplifying x + 3.2 = 2.332380758 Reorder the terms: 3.2 + x = 2.332380758 Solving 3.2 + x = 2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 2.332380758 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 2.332380758 + -3.2 x = 2.332380758 + -3.2 Combine like terms: 2.332380758 + -3.2 = -0.867619242 x = -0.867619242 Simplifying x = -0.867619242Subproblem 2
x + 3.2 = -2.332380758 Simplifying x + 3.2 = -2.332380758 Reorder the terms: 3.2 + x = -2.332380758 Solving 3.2 + x = -2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -2.332380758 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -2.332380758 + -3.2 x = -2.332380758 + -3.2 Combine like terms: -2.332380758 + -3.2 = -5.532380758 x = -5.532380758 Simplifying x = -5.532380758Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.867619242, -5.532380758}
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