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Simplifying 5x2 + 25x + 24 = 0 Reorder the terms: 24 + 25x + 5x2 = 0 Solving 24 + 25x + 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 + 5x + x2 = 0 Move the constant term to the right: Add '-4.8' to each side of the equation. 4.8 + 5x + -4.8 + x2 = 0 + -4.8 Reorder the terms: 4.8 + -4.8 + 5x + x2 = 0 + -4.8 Combine like terms: 4.8 + -4.8 = 0.0 0.0 + 5x + x2 = 0 + -4.8 5x + x2 = 0 + -4.8 Combine like terms: 0 + -4.8 = -4.8 5x + x2 = -4.8 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -4.8 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -4.8 + 6.25 Combine like terms: -4.8 + 6.25 = 1.45 6.25 + 5x + x2 = 1.45 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + 2.5) equal to 1.204159458 and -1.204159458.Subproblem 1
x + 2.5 = 1.204159458 Simplifying x + 2.5 = 1.204159458 Reorder the terms: 2.5 + x = 1.204159458 Solving 2.5 + x = 1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.204159458 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.204159458 + -2.5 x = 1.204159458 + -2.5 Combine like terms: 1.204159458 + -2.5 = -1.295840542 x = -1.295840542 Simplifying x = -1.295840542Subproblem 2
x + 2.5 = -1.204159458 Simplifying x + 2.5 = -1.204159458 Reorder the terms: 2.5 + x = -1.204159458 Solving 2.5 + x = -1.204159458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.204159458 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.204159458 + -2.5 x = -1.204159458 + -2.5 Combine like terms: -1.204159458 + -2.5 = -3.704159458 x = -3.704159458 Simplifying x = -3.704159458Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.295840542, -3.704159458}
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