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Simplifying 3x2 + -8x + -19 = x2 + 1 Reorder the terms: -19 + -8x + 3x2 = x2 + 1 Reorder the terms: -19 + -8x + 3x2 = 1 + x2 Solving -19 + -8x + 3x2 = 1 + x2 Solving for variable 'x'. Reorder the terms: -19 + -1 + -8x + 3x2 + -1x2 = 1 + x2 + -1 + -1x2 Combine like terms: -19 + -1 = -20 -20 + -8x + 3x2 + -1x2 = 1 + x2 + -1 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -20 + -8x + 2x2 = 1 + x2 + -1 + -1x2 Reorder the terms: -20 + -8x + 2x2 = 1 + -1 + x2 + -1x2 Combine like terms: 1 + -1 = 0 -20 + -8x + 2x2 = 0 + x2 + -1x2 -20 + -8x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + -8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -4x + x2)' equal to zero and attempt to solve: Simplifying -10 + -4x + x2 = 0 Solving -10 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4x + x2 = 0 + 10 -4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4x + x2 = 10 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 10 + 4 Reorder the terms: 4 + -4x + x2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4x + x2 = 14 Factor a perfect square on the left side: (x + -2)(x + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -2 = 3.741657387 Simplifying x + -2 = 3.741657387 Reorder the terms: -2 + x = 3.741657387 Solving -2 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.741657387 + 2 x = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 x = 5.741657387 Simplifying x = 5.741657387Subproblem 2
x + -2 = -3.741657387 Simplifying x + -2 = -3.741657387 Reorder the terms: -2 + x = -3.741657387 Solving -2 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.741657387 + 2 x = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 x = -1.741657387 Simplifying x = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.741657387, -1.741657387}Solution
x = {5.741657387, -1.741657387}
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