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Simplifying (1.293x + x2) = 19 Remove parenthesis around (1.293x + x2) 1.293x + x2 = 19 Solving 1.293x + x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 1.293x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 1.293x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 1.293x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 1.293x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 1.293x + x2 = 0 + 19 1.293x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 1.293x + x2 = 19 The x term is 1.293x. Take half its coefficient (0.6465). Square it (0.41796225) and add it to both sides. Add '0.41796225' to each side of the equation. 1.293x + 0.41796225 + x2 = 19 + 0.41796225 Reorder the terms: 0.41796225 + 1.293x + x2 = 19 + 0.41796225 Combine like terms: 19 + 0.41796225 = 19.41796225 0.41796225 + 1.293x + x2 = 19.41796225 Factor a perfect square on the left side: (x + 0.6465)(x + 0.6465) = 19.41796225 Calculate the square root of the right side: 4.406581697 Break this problem into two subproblems by setting (x + 0.6465) equal to 4.406581697 and -4.406581697.Subproblem 1
x + 0.6465 = 4.406581697 Simplifying x + 0.6465 = 4.406581697 Reorder the terms: 0.6465 + x = 4.406581697 Solving 0.6465 + x = 4.406581697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6465' to each side of the equation. 0.6465 + -0.6465 + x = 4.406581697 + -0.6465 Combine like terms: 0.6465 + -0.6465 = 0.0000 0.0000 + x = 4.406581697 + -0.6465 x = 4.406581697 + -0.6465 Combine like terms: 4.406581697 + -0.6465 = 3.760081697 x = 3.760081697 Simplifying x = 3.760081697Subproblem 2
x + 0.6465 = -4.406581697 Simplifying x + 0.6465 = -4.406581697 Reorder the terms: 0.6465 + x = -4.406581697 Solving 0.6465 + x = -4.406581697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6465' to each side of the equation. 0.6465 + -0.6465 + x = -4.406581697 + -0.6465 Combine like terms: 0.6465 + -0.6465 = 0.0000 0.0000 + x = -4.406581697 + -0.6465 x = -4.406581697 + -0.6465 Combine like terms: -4.406581697 + -0.6465 = -5.053081697 x = -5.053081697 Simplifying x = -5.053081697Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.760081697, -5.053081697}
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