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Simplifying 12x = -5x2 + -1 Reorder the terms: 12x = -1 + -5x2 Solving 12x = -1 + -5x2 Solving for variable 'x'. Reorder the terms: 1 + 12x + 5x2 = -1 + -5x2 + 1 + 5x2 Reorder the terms: 1 + 12x + 5x2 = -1 + 1 + -5x2 + 5x2 Combine like terms: -1 + 1 = 0 1 + 12x + 5x2 = 0 + -5x2 + 5x2 1 + 12x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 1 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2.4x + x2 = 0 + -0.2 2.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2.4x + x2 = -0.2 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -0.2 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -0.2 + 1.44 Combine like terms: -0.2 + 1.44 = 1.24 1.44 + 2.4x + x2 = 1.24 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + 1.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + 1.2 = 1.113552873 Simplifying x + 1.2 = 1.113552873 Reorder the terms: 1.2 + x = 1.113552873 Solving 1.2 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.113552873 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.113552873 + -1.2 x = 1.113552873 + -1.2 Combine like terms: 1.113552873 + -1.2 = -0.086447127 x = -0.086447127 Simplifying x = -0.086447127Subproblem 2
x + 1.2 = -1.113552873 Simplifying x + 1.2 = -1.113552873 Reorder the terms: 1.2 + x = -1.113552873 Solving 1.2 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.113552873 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.113552873 + -1.2 x = -1.113552873 + -1.2 Combine like terms: -1.113552873 + -1.2 = -2.313552873 x = -2.313552873 Simplifying x = -2.313552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.086447127, -2.313552873}
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