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Simplifying 3.8x2 + -6x + -9 = 0 Reorder the terms: -9 + -6x + 3.8x2 = 0 Solving -9 + -6x + 3.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.8 the coefficient of the squared term: Divide each side by '3.8'. -2.368421053 + -1.578947368x + x2 = 0 Move the constant term to the right: Add '2.368421053' to each side of the equation. -2.368421053 + -1.578947368x + 2.368421053 + x2 = 0 + 2.368421053 Reorder the terms: -2.368421053 + 2.368421053 + -1.578947368x + x2 = 0 + 2.368421053 Combine like terms: -2.368421053 + 2.368421053 = 0.000000000 0.000000000 + -1.578947368x + x2 = 0 + 2.368421053 -1.578947368x + x2 = 0 + 2.368421053 Combine like terms: 0 + 2.368421053 = 2.368421053 -1.578947368x + x2 = 2.368421053 The x term is -1.578947368x. Take half its coefficient (-0.789473684). Square it (0.6232686977) and add it to both sides. Add '0.6232686977' to each side of the equation. -1.578947368x + 0.6232686977 + x2 = 2.368421053 + 0.6232686977 Reorder the terms: 0.6232686977 + -1.578947368x + x2 = 2.368421053 + 0.6232686977 Combine like terms: 2.368421053 + 0.6232686977 = 2.9916897507 0.6232686977 + -1.578947368x + x2 = 2.9916897507 Factor a perfect square on the left side: (x + -0.789473684)(x + -0.789473684) = 2.9916897507 Calculate the square root of the right side: 1.729650182 Break this problem into two subproblems by setting (x + -0.789473684) equal to 1.729650182 and -1.729650182.Subproblem 1
x + -0.789473684 = 1.729650182 Simplifying x + -0.789473684 = 1.729650182 Reorder the terms: -0.789473684 + x = 1.729650182 Solving -0.789473684 + x = 1.729650182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.789473684' to each side of the equation. -0.789473684 + 0.789473684 + x = 1.729650182 + 0.789473684 Combine like terms: -0.789473684 + 0.789473684 = 0.000000000 0.000000000 + x = 1.729650182 + 0.789473684 x = 1.729650182 + 0.789473684 Combine like terms: 1.729650182 + 0.789473684 = 2.519123866 x = 2.519123866 Simplifying x = 2.519123866Subproblem 2
x + -0.789473684 = -1.729650182 Simplifying x + -0.789473684 = -1.729650182 Reorder the terms: -0.789473684 + x = -1.729650182 Solving -0.789473684 + x = -1.729650182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.789473684' to each side of the equation. -0.789473684 + 0.789473684 + x = -1.729650182 + 0.789473684 Combine like terms: -0.789473684 + 0.789473684 = 0.000000000 0.000000000 + x = -1.729650182 + 0.789473684 x = -1.729650182 + 0.789473684 Combine like terms: -1.729650182 + 0.789473684 = -0.940176498 x = -0.940176498 Simplifying x = -0.940176498Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.519123866, -0.940176498}
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