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Simplifying x2 + -2.034x + -2.898 = 0 Reorder the terms: -2.898 + -2.034x + x2 = 0 Solving -2.898 + -2.034x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2.898' to each side of the equation. -2.898 + -2.034x + 2.898 + x2 = 0 + 2.898 Reorder the terms: -2.898 + 2.898 + -2.034x + x2 = 0 + 2.898 Combine like terms: -2.898 + 2.898 = 0.000 0.000 + -2.034x + x2 = 0 + 2.898 -2.034x + x2 = 0 + 2.898 Combine like terms: 0 + 2.898 = 2.898 -2.034x + x2 = 2.898 The x term is -2.034x. Take half its coefficient (-1.017). Square it (1.034289) and add it to both sides. Add '1.034289' to each side of the equation. -2.034x + 1.034289 + x2 = 2.898 + 1.034289 Reorder the terms: 1.034289 + -2.034x + x2 = 2.898 + 1.034289 Combine like terms: 2.898 + 1.034289 = 3.932289 1.034289 + -2.034x + x2 = 3.932289 Factor a perfect square on the left side: (x + -1.017)(x + -1.017) = 3.932289 Calculate the square root of the right side: 1.983 Break this problem into two subproblems by setting (x + -1.017) equal to 1.983 and -1.983.Subproblem 1
x + -1.017 = 1.983 Simplifying x + -1.017 = 1.983 Reorder the terms: -1.017 + x = 1.983 Solving -1.017 + x = 1.983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.017' to each side of the equation. -1.017 + 1.017 + x = 1.983 + 1.017 Combine like terms: -1.017 + 1.017 = 0.000 0.000 + x = 1.983 + 1.017 x = 1.983 + 1.017 Combine like terms: 1.983 + 1.017 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.017 = -1.983 Simplifying x + -1.017 = -1.983 Reorder the terms: -1.017 + x = -1.983 Solving -1.017 + x = -1.983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.017' to each side of the equation. -1.017 + 1.017 + x = -1.983 + 1.017 Combine like terms: -1.017 + 1.017 = 0.000 0.000 + x = -1.983 + 1.017 x = -1.983 + 1.017 Combine like terms: -1.983 + 1.017 = -0.966 x = -0.966 Simplifying x = -0.966Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -0.966}
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