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Simplifying 4x2 + 20x + 19 = 0 Reorder the terms: 19 + 20x + 4x2 = 0 Solving 19 + 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'. 4.75 + 5x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + 5x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + 5x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + 5x + x2 = 0 + -4.75 5x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 5x + x2 = -4.75 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 = -4.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -4.75 + 6.25 Combine like terms: -4.75 + 6.25 = 1.5 6.25 + 5x + x2 = 1.5 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + 2.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + 2.5 = 1.224744871 Simplifying x + 2.5 = 1.224744871 Reorder the terms: 2.5 + x = 1.224744871 Solving 2.5 + x = 1.224744871 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 = 1.224744871 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.224744871 + -2.5 x = 1.224744871 + -2.5 Combine like terms: 1.224744871 + -2.5 = -1.275255129 x = -1.275255129 Simplifying x = -1.275255129Subproblem 2
x + 2.5 = -1.224744871 Simplifying x + 2.5 = -1.224744871 Reorder the terms: 2.5 + x = -1.224744871 Solving 2.5 + x = -1.224744871 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 = -1.224744871 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.224744871 + -2.5 x = -1.224744871 + -2.5 Combine like terms: -1.224744871 + -2.5 = -3.724744871 x = -3.724744871 Simplifying x = -3.724744871Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.275255129, -3.724744871}
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