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Simplifying 5x2 + 22x = -18 Reorder the terms: 22x + 5x2 = -18 Solving 22x + 5x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + 22x + 5x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + 4.4x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + 4.4x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + 4.4x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + 4.4x + x2 = 0 + -3.6 4.4x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 4.4x + x2 = -3.6 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 = -3.6 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -3.6 + 4.84 Combine like terms: -3.6 + 4.84 = 1.24 4.84 + 4.4x + x2 = 1.24 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + 2.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + 2.2 = 1.113552873 Simplifying x + 2.2 = 1.113552873 Reorder the terms: 2.2 + x = 1.113552873 Solving 2.2 + x = 1.113552873 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 = 1.113552873 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 1.113552873 + -2.2 x = 1.113552873 + -2.2 Combine like terms: 1.113552873 + -2.2 = -1.086447127 x = -1.086447127 Simplifying x = -1.086447127Subproblem 2
x + 2.2 = -1.113552873 Simplifying x + 2.2 = -1.113552873 Reorder the terms: 2.2 + x = -1.113552873 Solving 2.2 + x = -1.113552873 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 = -1.113552873 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -1.113552873 + -2.2 x = -1.113552873 + -2.2 Combine like terms: -1.113552873 + -2.2 = -3.313552873 x = -3.313552873 Simplifying x = -3.313552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.086447127, -3.313552873}
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