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Simplifying (x2) + 3.4x + -26.01 = 0 x2 + 3.4x + -26.01 = 0 Reorder the terms: -26.01 + 3.4x + x2 = 0 Solving -26.01 + 3.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '26.01' to each side of the equation. -26.01 + 3.4x + 26.01 + x2 = 0 + 26.01 Reorder the terms: -26.01 + 26.01 + 3.4x + x2 = 0 + 26.01 Combine like terms: -26.01 + 26.01 = 0.00 0.00 + 3.4x + x2 = 0 + 26.01 3.4x + x2 = 0 + 26.01 Combine like terms: 0 + 26.01 = 26.01 3.4x + x2 = 26.01 The x term is 3.4x. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4x + 2.89 + x2 = 26.01 + 2.89 Reorder the terms: 2.89 + 3.4x + x2 = 26.01 + 2.89 Combine like terms: 26.01 + 2.89 = 28.9 2.89 + 3.4x + x2 = 28.9 Factor a perfect square on the left side: (x + 1.7)(x + 1.7) = 28.9 Calculate the square root of the right side: 5.375872022 Break this problem into two subproblems by setting (x + 1.7) equal to 5.375872022 and -5.375872022.Subproblem 1
x + 1.7 = 5.375872022 Simplifying x + 1.7 = 5.375872022 Reorder the terms: 1.7 + x = 5.375872022 Solving 1.7 + x = 5.375872022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 5.375872022 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 5.375872022 + -1.7 x = 5.375872022 + -1.7 Combine like terms: 5.375872022 + -1.7 = 3.675872022 x = 3.675872022 Simplifying x = 3.675872022Subproblem 2
x + 1.7 = -5.375872022 Simplifying x + 1.7 = -5.375872022 Reorder the terms: 1.7 + x = -5.375872022 Solving 1.7 + x = -5.375872022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -5.375872022 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -5.375872022 + -1.7 x = -5.375872022 + -1.7 Combine like terms: -5.375872022 + -1.7 = -7.075872022 x = -7.075872022 Simplifying x = -7.075872022Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.675872022, -7.075872022}
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