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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 = 0.329165038 x = 0.329165038 Simplifying x = 0.329165038Subproblem 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 = -10.329165038 x = -10.329165038 Simplifying x = -10.329165038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.329165038, -10.329165038}
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