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Simplifying 4x2 + 20x + -0.12 = 0 Reorder the terms: -0.12 + 20x + 4x2 = 0 Solving -0.12 + 20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.03 + 5x + x2 = 0 Move the constant term to the right: Add '0.03' to each side of the equation. -0.03 + 5x + 0.03 + x2 = 0 + 0.03 Reorder the terms: -0.03 + 0.03 + 5x + x2 = 0 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + 5x + x2 = 0 + 0.03 5x + x2 = 0 + 0.03 Combine like terms: 0 + 0.03 = 0.03 5x + x2 = 0.03 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.03 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.03 + 6.25 Combine like terms: 0.03 + 6.25 = 6.28 6.25 + 5x + x2 = 6.28 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.28 Calculate the square root of the right side: 2.505992817 Break this problem into two subproblems by setting (x + 2.5) equal to 2.505992817 and -2.505992817.Subproblem 1
x + 2.5 = 2.505992817 Simplifying x + 2.5 = 2.505992817 Reorder the terms: 2.5 + x = 2.505992817 Solving 2.5 + x = 2.505992817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.505992817 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.505992817 + -2.5 x = 2.505992817 + -2.5 Combine like terms: 2.505992817 + -2.5 = 0.005992817 x = 0.005992817 Simplifying x = 0.005992817Subproblem 2
x + 2.5 = -2.505992817 Simplifying x + 2.5 = -2.505992817 Reorder the terms: 2.5 + x = -2.505992817 Solving 2.5 + x = -2.505992817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.505992817 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.505992817 + -2.5 x = -2.505992817 + -2.5 Combine like terms: -2.505992817 + -2.5 = -5.005992817 x = -5.005992817 Simplifying x = -5.005992817Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.005992817, -5.005992817}
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