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Simplifying 4x2 + 19x + -20 = 0 Reorder the terms: -20 + 19x + 4x2 = 0 Solving -20 + 19x + 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'. -5 + 4.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 4.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 4.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4.75x + x2 = 0 + 5 4.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 4.75x + x2 = 5 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 5 + 5.640625 Combine like terms: 5 + 5.640625 = 10.640625 5.640625 + 4.75x + x2 = 10.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 10.640625 Calculate the square root of the right side: 3.261997088 Break this problem into two subproblems by setting (x + 2.375) equal to 3.261997088 and -3.261997088.Subproblem 1
x + 2.375 = 3.261997088 Simplifying x + 2.375 = 3.261997088 Reorder the terms: 2.375 + x = 3.261997088 Solving 2.375 + x = 3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 3.261997088 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.261997088 + -2.375 x = 3.261997088 + -2.375 Combine like terms: 3.261997088 + -2.375 = 0.886997088 x = 0.886997088 Simplifying x = 0.886997088Subproblem 2
x + 2.375 = -3.261997088 Simplifying x + 2.375 = -3.261997088 Reorder the terms: 2.375 + x = -3.261997088 Solving 2.375 + x = -3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -3.261997088 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.261997088 + -2.375 x = -3.261997088 + -2.375 Combine like terms: -3.261997088 + -2.375 = -5.636997088 x = -5.636997088 Simplifying x = -5.636997088Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.886997088, -5.636997088}
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