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Simplifying x2 + 2.23x + -3 = 0 Reorder the terms: -3 + 2.23x + x2 = 0 Solving -3 + 2.23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.23x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.23x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.23x + x2 = 0 + 3 2.23x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.23x + x2 = 3 The x term is 2.23x. Take half its coefficient (1.115). Square it (1.243225) and add it to both sides. Add '1.243225' to each side of the equation. 2.23x + 1.243225 + x2 = 3 + 1.243225 Reorder the terms: 1.243225 + 2.23x + x2 = 3 + 1.243225 Combine like terms: 3 + 1.243225 = 4.243225 1.243225 + 2.23x + x2 = 4.243225 Factor a perfect square on the left side: (x + 1.115)(x + 1.115) = 4.243225 Calculate the square root of the right side: 2.059908979 Break this problem into two subproblems by setting (x + 1.115) equal to 2.059908979 and -2.059908979.Subproblem 1
x + 1.115 = 2.059908979 Simplifying x + 1.115 = 2.059908979 Reorder the terms: 1.115 + x = 2.059908979 Solving 1.115 + x = 2.059908979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.115' to each side of the equation. 1.115 + -1.115 + x = 2.059908979 + -1.115 Combine like terms: 1.115 + -1.115 = 0.000 0.000 + x = 2.059908979 + -1.115 x = 2.059908979 + -1.115 Combine like terms: 2.059908979 + -1.115 = 0.944908979 x = 0.944908979 Simplifying x = 0.944908979Subproblem 2
x + 1.115 = -2.059908979 Simplifying x + 1.115 = -2.059908979 Reorder the terms: 1.115 + x = -2.059908979 Solving 1.115 + x = -2.059908979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.115' to each side of the equation. 1.115 + -1.115 + x = -2.059908979 + -1.115 Combine like terms: 1.115 + -1.115 = 0.000 0.000 + x = -2.059908979 + -1.115 x = -2.059908979 + -1.115 Combine like terms: -2.059908979 + -1.115 = -3.174908979 x = -3.174908979 Simplifying x = -3.174908979Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.944908979, -3.174908979}
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