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Simplifying 4x2 + 20x + 19 = 6 Reorder the terms: 19 + 20x + 4x2 = 6 Solving 19 + 20x + 4x2 = 6 Solving for variable 'x'. Reorder the terms: 19 + -6 + 20x + 4x2 = 6 + -6 Combine like terms: 19 + -6 = 13 13 + 20x + 4x2 = 6 + -6 Combine like terms: 6 + -6 = 0 13 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 5x + x2 = 0 + -3.25 5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 5x + x2 = -3.25 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 = -3.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3.25 + 6.25 Combine like terms: -3.25 + 6.25 = 3 6.25 + 5x + x2 = 3 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 2.5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 2.5 = 1.732050808 Simplifying x + 2.5 = 1.732050808 Reorder the terms: 2.5 + x = 1.732050808 Solving 2.5 + x = 1.732050808 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 = 1.732050808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.732050808 + -2.5 x = 1.732050808 + -2.5 Combine like terms: 1.732050808 + -2.5 = -0.767949192 x = -0.767949192 Simplifying x = -0.767949192Subproblem 2
x + 2.5 = -1.732050808 Simplifying x + 2.5 = -1.732050808 Reorder the terms: 2.5 + x = -1.732050808 Solving 2.5 + x = -1.732050808 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 = -1.732050808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.732050808 + -2.5 x = -1.732050808 + -2.5 Combine like terms: -1.732050808 + -2.5 = -4.232050808 x = -4.232050808 Simplifying x = -4.232050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.767949192, -4.232050808}
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