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Simplifying 4x2 + -8x + -19 = 0 Reorder the terms: -19 + -8x + 4x2 = 0 Solving -19 + -8x + 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 + -2x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -2x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -2x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -2x + x2 = 0 + 4.75 -2x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -2x + x2 = 4.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 4.75 + 1 Reorder the terms: 1 + -2x + x2 = 4.75 + 1 Combine like terms: 4.75 + 1 = 5.75 1 + -2x + x2 = 5.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + -1) equal to 2.397915762 and -2.397915762.Subproblem 1
x + -1 = 2.397915762 Simplifying x + -1 = 2.397915762 Reorder the terms: -1 + x = 2.397915762 Solving -1 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.397915762 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.397915762 + 1 x = 2.397915762 + 1 Combine like terms: 2.397915762 + 1 = 3.397915762 x = 3.397915762 Simplifying x = 3.397915762Subproblem 2
x + -1 = -2.397915762 Simplifying x + -1 = -2.397915762 Reorder the terms: -1 + x = -2.397915762 Solving -1 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.397915762 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.397915762 + 1 x = -2.397915762 + 1 Combine like terms: -2.397915762 + 1 = -1.397915762 x = -1.397915762 Simplifying x = -1.397915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.397915762, -1.397915762}
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