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Simplifying 5x2 + 36x + 24 = 0 Reorder the terms: 24 + 36x + 5x2 = 0 Solving 24 + 36x + 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 + 7.2x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 7.2x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 7.2x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 7.2x + x2 = 0 + -4.8 7.2x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 7.2x + x2 = -4.8 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = -4.8 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = -4.8 + 12.96 Combine like terms: -4.8 + 12.96 = 8.16 12.96 + 7.2x + x2 = 8.16 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 8.16 Calculate the square root of the right side: 2.856571371 Break this problem into two subproblems by setting (x + 3.6) equal to 2.856571371 and -2.856571371.Subproblem 1
x + 3.6 = 2.856571371 Simplifying x + 3.6 = 2.856571371 Reorder the terms: 3.6 + x = 2.856571371 Solving 3.6 + x = 2.856571371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 2.856571371 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 2.856571371 + -3.6 x = 2.856571371 + -3.6 Combine like terms: 2.856571371 + -3.6 = -0.743428629 x = -0.743428629 Simplifying x = -0.743428629Subproblem 2
x + 3.6 = -2.856571371 Simplifying x + 3.6 = -2.856571371 Reorder the terms: 3.6 + x = -2.856571371 Solving 3.6 + x = -2.856571371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -2.856571371 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -2.856571371 + -3.6 x = -2.856571371 + -3.6 Combine like terms: -2.856571371 + -3.6 = -6.456571371 x = -6.456571371 Simplifying x = -6.456571371Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.743428629, -6.456571371}
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