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Simplifying x2 + -10x + -3.4 = 0 Reorder the terms: -3.4 + -10x + x2 = 0 Solving -3.4 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -10x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -10x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -10x + x2 = 0 + 3.4 -10x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -10x + x2 = 3.4 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 3.4 + 25 Reorder the terms: 25 + -10x + x2 = 3.4 + 25 Combine like terms: 3.4 + 25 = 28.4 25 + -10x + x2 = 28.4 Factor a perfect square on the left side: (x + -5)(x + -5) = 28.4 Calculate the square root of the right side: 5.329165038 Break this problem into two subproblems by setting (x + -5) equal to 5.329165038 and -5.329165038.Subproblem 1
x + -5 = 5.329165038 Simplifying x + -5 = 5.329165038 Reorder the terms: -5 + x = 5.329165038 Solving -5 + x = 5.329165038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.329165038 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.329165038 + 5 x = 5.329165038 + 5 Combine like terms: 5.329165038 + 5 = 10.329165038 x = 10.329165038 Simplifying x = 10.329165038Subproblem 2
x + -5 = -5.329165038 Simplifying x + -5 = -5.329165038 Reorder the terms: -5 + x = -5.329165038 Solving -5 + x = -5.329165038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.329165038 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.329165038 + 5 x = -5.329165038 + 5 Combine like terms: -5.329165038 + 5 = -0.329165038 x = -0.329165038 Simplifying x = -0.329165038Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.329165038, -0.329165038}
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