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Simplifying x2 + -0.67x + -2.89 = 0 Reorder the terms: -2.89 + -0.67x + x2 = 0 Solving -2.89 + -0.67x + 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 + -0.67x + 2.89 + x2 = 0 + 2.89 Reorder the terms: -2.89 + 2.89 + -0.67x + x2 = 0 + 2.89 Combine like terms: -2.89 + 2.89 = 0.00 0.00 + -0.67x + x2 = 0 + 2.89 -0.67x + x2 = 0 + 2.89 Combine like terms: 0 + 2.89 = 2.89 -0.67x + x2 = 2.89 The x term is -0.67x. Take half its coefficient (-0.335). Square it (0.112225) and add it to both sides. Add '0.112225' to each side of the equation. -0.67x + 0.112225 + x2 = 2.89 + 0.112225 Reorder the terms: 0.112225 + -0.67x + x2 = 2.89 + 0.112225 Combine like terms: 2.89 + 0.112225 = 3.002225 0.112225 + -0.67x + x2 = 3.002225 Factor a perfect square on the left side: (x + -0.335)(x + -0.335) = 3.002225 Calculate the square root of the right side: 1.732692991 Break this problem into two subproblems by setting (x + -0.335) equal to 1.732692991 and -1.732692991.Subproblem 1
x + -0.335 = 1.732692991 Simplifying x + -0.335 = 1.732692991 Reorder the terms: -0.335 + x = 1.732692991 Solving -0.335 + x = 1.732692991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335' to each side of the equation. -0.335 + 0.335 + x = 1.732692991 + 0.335 Combine like terms: -0.335 + 0.335 = 0.000 0.000 + x = 1.732692991 + 0.335 x = 1.732692991 + 0.335 Combine like terms: 1.732692991 + 0.335 = 2.067692991 x = 2.067692991 Simplifying x = 2.067692991Subproblem 2
x + -0.335 = -1.732692991 Simplifying x + -0.335 = -1.732692991 Reorder the terms: -0.335 + x = -1.732692991 Solving -0.335 + x = -1.732692991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.335' to each side of the equation. -0.335 + 0.335 + x = -1.732692991 + 0.335 Combine like terms: -0.335 + 0.335 = 0.000 0.000 + x = -1.732692991 + 0.335 x = -1.732692991 + 0.335 Combine like terms: -1.732692991 + 0.335 = -1.397692991 x = -1.397692991 Simplifying x = -1.397692991Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.067692991, -1.397692991}
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