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Simplifying 10x2 + 40x + 4 = 0 Reorder the terms: 4 + 40x + 10x2 = 0 Solving 4 + 40x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 20x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 20x + 5x2 = 0 Solving 2 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 4x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 4x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 4x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 4x + x2 = 0 + -0.4 4x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 4x + x2 = -0.4 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 = -0.4 + 4 Reorder the terms: 4 + 4x + x2 = -0.4 + 4 Combine like terms: -0.4 + 4 = 3.6 4 + 4x + x2 = 3.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (x + 2) equal to 1.897366596 and -1.897366596.Subproblem 1
x + 2 = 1.897366596 Simplifying x + 2 = 1.897366596 Reorder the terms: 2 + x = 1.897366596 Solving 2 + x = 1.897366596 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 = 1.897366596 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.897366596 + -2 x = 1.897366596 + -2 Combine like terms: 1.897366596 + -2 = -0.102633404 x = -0.102633404 Simplifying x = -0.102633404Subproblem 2
x + 2 = -1.897366596 Simplifying x + 2 = -1.897366596 Reorder the terms: 2 + x = -1.897366596 Solving 2 + x = -1.897366596 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 = -1.897366596 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.897366596 + -2 x = -1.897366596 + -2 Combine like terms: -1.897366596 + -2 = -3.897366596 x = -3.897366596 Simplifying x = -3.897366596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.102633404, -3.897366596}Solution
x = {-0.102633404, -3.897366596}
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