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Simplifying x2 + -13.26x + 28 = 0 Reorder the terms: 28 + -13.26x + x2 = 0 Solving 28 + -13.26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -13.26x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -13.26x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -13.26x + x2 = 0 + -28 -13.26x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -13.26x + x2 = -28 The x term is -13.26x. Take half its coefficient (-6.63). Square it (43.9569) and add it to both sides. Add '43.9569' to each side of the equation. -13.26x + 43.9569 + x2 = -28 + 43.9569 Reorder the terms: 43.9569 + -13.26x + x2 = -28 + 43.9569 Combine like terms: -28 + 43.9569 = 15.9569 43.9569 + -13.26x + x2 = 15.9569 Factor a perfect square on the left side: (x + -6.63)(x + -6.63) = 15.9569 Calculate the square root of the right side: 3.994608867 Break this problem into two subproblems by setting (x + -6.63) equal to 3.994608867 and -3.994608867.Subproblem 1
x + -6.63 = 3.994608867 Simplifying x + -6.63 = 3.994608867 Reorder the terms: -6.63 + x = 3.994608867 Solving -6.63 + x = 3.994608867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.63' to each side of the equation. -6.63 + 6.63 + x = 3.994608867 + 6.63 Combine like terms: -6.63 + 6.63 = 0.00 0.00 + x = 3.994608867 + 6.63 x = 3.994608867 + 6.63 Combine like terms: 3.994608867 + 6.63 = 10.624608867 x = 10.624608867 Simplifying x = 10.624608867Subproblem 2
x + -6.63 = -3.994608867 Simplifying x + -6.63 = -3.994608867 Reorder the terms: -6.63 + x = -3.994608867 Solving -6.63 + x = -3.994608867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.63' to each side of the equation. -6.63 + 6.63 + x = -3.994608867 + 6.63 Combine like terms: -6.63 + 6.63 = 0.00 0.00 + x = -3.994608867 + 6.63 x = -3.994608867 + 6.63 Combine like terms: -3.994608867 + 6.63 = 2.635391133 x = 2.635391133 Simplifying x = 2.635391133Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.624608867, 2.635391133}
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