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Simplifying x2 + 2.645x + -3 = 0 Reorder the terms: -3 + 2.645x + x2 = 0 Solving -3 + 2.645x + 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 + 2.645x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.645x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.645x + x2 = 0 + 3 2.645x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.645x + x2 = 3 The x term is 2.645x. Take half its coefficient (1.3225). Square it (1.74900625) and add it to both sides. Add '1.74900625' to each side of the equation. 2.645x + 1.74900625 + x2 = 3 + 1.74900625 Reorder the terms: 1.74900625 + 2.645x + x2 = 3 + 1.74900625 Combine like terms: 3 + 1.74900625 = 4.74900625 1.74900625 + 2.645x + x2 = 4.74900625 Factor a perfect square on the left side: (x + 1.3225)(x + 1.3225) = 4.74900625 Calculate the square root of the right side: 2.179221478 Break this problem into two subproblems by setting (x + 1.3225) equal to 2.179221478 and -2.179221478.Subproblem 1
x + 1.3225 = 2.179221478 Simplifying x + 1.3225 = 2.179221478 Reorder the terms: 1.3225 + x = 2.179221478 Solving 1.3225 + x = 2.179221478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3225' to each side of the equation. 1.3225 + -1.3225 + x = 2.179221478 + -1.3225 Combine like terms: 1.3225 + -1.3225 = 0.0000 0.0000 + x = 2.179221478 + -1.3225 x = 2.179221478 + -1.3225 Combine like terms: 2.179221478 + -1.3225 = 0.856721478 x = 0.856721478 Simplifying x = 0.856721478Subproblem 2
x + 1.3225 = -2.179221478 Simplifying x + 1.3225 = -2.179221478 Reorder the terms: 1.3225 + x = -2.179221478 Solving 1.3225 + x = -2.179221478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3225' to each side of the equation. 1.3225 + -1.3225 + x = -2.179221478 + -1.3225 Combine like terms: 1.3225 + -1.3225 = 0.0000 0.0000 + x = -2.179221478 + -1.3225 x = -2.179221478 + -1.3225 Combine like terms: -2.179221478 + -1.3225 = -3.501721478 x = -3.501721478 Simplifying x = -3.501721478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.856721478, -3.501721478}
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