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Simplifying 4x2 + -20x = 0.24 Reorder the terms: -20x + 4x2 = 0.24 Solving -20x + 4x2 = 0.24 Solving for variable 'x'. Reorder the terms: -0.24 + -20x + 4x2 = 0.24 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 -0.24 + -20x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.06 + -5x + x2 = 0.00 Move the constant term to the right: Add '0.06' to each side of the equation. -0.06 + -5x + 0.06 + x2 = 0.00 + 0.06 Reorder the terms: -0.06 + 0.06 + -5x + x2 = 0.00 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + -5x + x2 = 0.00 + 0.06 -5x + x2 = 0.00 + 0.06 Combine like terms: 0.00 + 0.06 = 0.06 -5x + x2 = 0.06 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 = 0.06 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.06 + 6.25 Combine like terms: 0.06 + 6.25 = 6.31 6.25 + -5x + x2 = 6.31 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.31 Calculate the square root of the right side: 2.511971337 Break this problem into two subproblems by setting (x + -2.5) equal to 2.511971337 and -2.511971337.Subproblem 1
x + -2.5 = 2.511971337 Simplifying x + -2.5 = 2.511971337 Reorder the terms: -2.5 + x = 2.511971337 Solving -2.5 + x = 2.511971337 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 = 2.511971337 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.511971337 + 2.5 x = 2.511971337 + 2.5 Combine like terms: 2.511971337 + 2.5 = 5.011971337 x = 5.011971337 Simplifying x = 5.011971337Subproblem 2
x + -2.5 = -2.511971337 Simplifying x + -2.5 = -2.511971337 Reorder the terms: -2.5 + x = -2.511971337 Solving -2.5 + x = -2.511971337 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 = -2.511971337 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.511971337 + 2.5 x = -2.511971337 + 2.5 Combine like terms: -2.511971337 + 2.5 = -0.011971337 x = -0.011971337 Simplifying x = -0.011971337Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.011971337, -0.011971337}
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