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Simplifying 4x2 + -19x + -18 = 0 Reorder the terms: -18 + -19x + 4x2 = 0 Solving -18 + -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'. -4.5 + -4.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -4.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -4.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -4.75x + x2 = 0 + 4.5 -4.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -4.75x + x2 = 4.5 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 = 4.5 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = 4.5 + 5.640625 Combine like terms: 4.5 + 5.640625 = 10.140625 5.640625 + -4.75x + x2 = 10.140625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 10.140625 Calculate the square root of the right side: 3.184434801 Break this problem into two subproblems by setting (x + -2.375) equal to 3.184434801 and -3.184434801.Subproblem 1
x + -2.375 = 3.184434801 Simplifying x + -2.375 = 3.184434801 Reorder the terms: -2.375 + x = 3.184434801 Solving -2.375 + x = 3.184434801 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 = 3.184434801 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.184434801 + 2.375 x = 3.184434801 + 2.375 Combine like terms: 3.184434801 + 2.375 = 5.559434801 x = 5.559434801 Simplifying x = 5.559434801Subproblem 2
x + -2.375 = -3.184434801 Simplifying x + -2.375 = -3.184434801 Reorder the terms: -2.375 + x = -3.184434801 Solving -2.375 + x = -3.184434801 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 = -3.184434801 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.184434801 + 2.375 x = -3.184434801 + 2.375 Combine like terms: -3.184434801 + 2.375 = -0.809434801 x = -0.809434801 Simplifying x = -0.809434801Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.559434801, -0.809434801}
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