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Simplifying x2 + -6x + -21.9 = 0 Reorder the terms: -21.9 + -6x + x2 = 0 Solving -21.9 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21.9' to each side of the equation. -21.9 + -6x + 21.9 + x2 = 0 + 21.9 Reorder the terms: -21.9 + 21.9 + -6x + x2 = 0 + 21.9 Combine like terms: -21.9 + 21.9 = 0.0 0.0 + -6x + x2 = 0 + 21.9 -6x + x2 = 0 + 21.9 Combine like terms: 0 + 21.9 = 21.9 -6x + x2 = 21.9 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 21.9 + 9 Reorder the terms: 9 + -6x + x2 = 21.9 + 9 Combine like terms: 21.9 + 9 = 30.9 9 + -6x + x2 = 30.9 Factor a perfect square on the left side: (x + -3)(x + -3) = 30.9 Calculate the square root of the right side: 5.558776844 Break this problem into two subproblems by setting (x + -3) equal to 5.558776844 and -5.558776844.Subproblem 1
x + -3 = 5.558776844 Simplifying x + -3 = 5.558776844 Reorder the terms: -3 + x = 5.558776844 Solving -3 + x = 5.558776844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.558776844 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.558776844 + 3 x = 5.558776844 + 3 Combine like terms: 5.558776844 + 3 = 8.558776844 x = 8.558776844 Simplifying x = 8.558776844Subproblem 2
x + -3 = -5.558776844 Simplifying x + -3 = -5.558776844 Reorder the terms: -3 + x = -5.558776844 Solving -3 + x = -5.558776844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.558776844 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.558776844 + 3 x = -5.558776844 + 3 Combine like terms: -5.558776844 + 3 = -2.558776844 x = -2.558776844 Simplifying x = -2.558776844Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.558776844, -2.558776844}
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