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Simplifying 5x2 + 22x = 24 Reorder the terms: 22x + 5x2 = 24 Solving 22x + 5x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 22x + 5x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 4.4x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 4.4x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 4.4x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4.4x + x2 = 0 + 4.8 4.4x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 4.4x + x2 = 4.8 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 4.8 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 4.8 + 4.84 Combine like terms: 4.8 + 4.84 = 9.64 4.84 + 4.4x + x2 = 9.64 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 9.64 Calculate the square root of the right side: 3.104834939 Break this problem into two subproblems by setting (x + 2.2) equal to 3.104834939 and -3.104834939.Subproblem 1
x + 2.2 = 3.104834939 Simplifying x + 2.2 = 3.104834939 Reorder the terms: 2.2 + x = 3.104834939 Solving 2.2 + x = 3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 3.104834939 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 3.104834939 + -2.2 x = 3.104834939 + -2.2 Combine like terms: 3.104834939 + -2.2 = 0.904834939 x = 0.904834939 Simplifying x = 0.904834939Subproblem 2
x + 2.2 = -3.104834939 Simplifying x + 2.2 = -3.104834939 Reorder the terms: 2.2 + x = -3.104834939 Solving 2.2 + x = -3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -3.104834939 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -3.104834939 + -2.2 x = -3.104834939 + -2.2 Combine like terms: -3.104834939 + -2.2 = -5.304834939 x = -5.304834939 Simplifying x = -5.304834939Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.904834939, -5.304834939}
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