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Simplifying x2 + -2(2.8) * x + -6 = 0 Multiply -2 * 2.8 x2 + -5.6x + -6 = 0 Reorder the terms: -6 + -5.6x + x2 = 0 Solving -6 + -5.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -5.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -5.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5.6x + x2 = 0 + 6 -5.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5.6x + x2 = 6 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 6 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 6 + 7.84 Combine like terms: 6 + 7.84 = 13.84 7.84 + -5.6x + x2 = 13.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 13.84 Calculate the square root of the right side: 3.720215048 Break this problem into two subproblems by setting (x + -2.8) equal to 3.720215048 and -3.720215048.Subproblem 1
x + -2.8 = 3.720215048 Simplifying x + -2.8 = 3.720215048 Reorder the terms: -2.8 + x = 3.720215048 Solving -2.8 + x = 3.720215048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 3.720215048 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 3.720215048 + 2.8 x = 3.720215048 + 2.8 Combine like terms: 3.720215048 + 2.8 = 6.520215048 x = 6.520215048 Simplifying x = 6.520215048Subproblem 2
x + -2.8 = -3.720215048 Simplifying x + -2.8 = -3.720215048 Reorder the terms: -2.8 + x = -3.720215048 Solving -2.8 + x = -3.720215048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -3.720215048 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -3.720215048 + 2.8 x = -3.720215048 + 2.8 Combine like terms: -3.720215048 + 2.8 = -0.920215048 x = -0.920215048 Simplifying x = -0.920215048Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.520215048, -0.920215048}
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