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Simplifying 5x2 + 20x + 12 = 0 Reorder the terms: 12 + 20x + 5x2 = 0 Solving 12 + 20x + 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'. 2.4 + 4x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 4x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 4x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 4x + x2 = 0 + -2.4 4x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 4x + x2 = -2.4 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.4 + 4 Reorder the terms: 4 + 4x + x2 = -2.4 + 4 Combine like terms: -2.4 + 4 = 1.6 4 + 4x + x2 = 1.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (x + 2) equal to 1.264911064 and -1.264911064.Subproblem 1
x + 2 = 1.264911064 Simplifying x + 2 = 1.264911064 Reorder the terms: 2 + x = 1.264911064 Solving 2 + x = 1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.264911064 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.264911064 + -2 x = 1.264911064 + -2 Combine like terms: 1.264911064 + -2 = -0.735088936 x = -0.735088936 Simplifying x = -0.735088936Subproblem 2
x + 2 = -1.264911064 Simplifying x + 2 = -1.264911064 Reorder the terms: 2 + x = -1.264911064 Solving 2 + x = -1.264911064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.264911064 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.264911064 + -2 x = -1.264911064 + -2 Combine like terms: -1.264911064 + -2 = -3.264911064 x = -3.264911064 Simplifying x = -3.264911064Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.735088936, -3.264911064}
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