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