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Simplifying 38x2 + 120x = -45 Reorder the terms: 120x + 38x2 = -45 Solving 120x + 38x2 = -45 Solving for variable 'x'. Reorder the terms: 45 + 120x + 38x2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + 120x + 38x2 = 0 Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. 1.184210526 + 3.157894737x + x2 = 0 Move the constant term to the right: Add '-1.184210526' to each side of the equation. 1.184210526 + 3.157894737x + -1.184210526 + x2 = 0 + -1.184210526 Reorder the terms: 1.184210526 + -1.184210526 + 3.157894737x + x2 = 0 + -1.184210526 Combine like terms: 1.184210526 + -1.184210526 = 0.000000000 0.000000000 + 3.157894737x + x2 = 0 + -1.184210526 3.157894737x + x2 = 0 + -1.184210526 Combine like terms: 0 + -1.184210526 = -1.184210526 3.157894737x + x2 = -1.184210526 The x term is 3.157894737x. Take half its coefficient (1.578947369). Square it (2.493074794) and add it to both sides. Add '2.493074794' to each side of the equation. 3.157894737x + 2.493074794 + x2 = -1.184210526 + 2.493074794 Reorder the terms: 2.493074794 + 3.157894737x + x2 = -1.184210526 + 2.493074794 Combine like terms: -1.184210526 + 2.493074794 = 1.308864268 2.493074794 + 3.157894737x + x2 = 1.308864268 Factor a perfect square on the left side: (x + 1.578947369)(x + 1.578947369) = 1.308864268 Calculate the square root of the right side: 1.14405606 Break this problem into two subproblems by setting (x + 1.578947369) equal to 1.14405606 and -1.14405606.Subproblem 1
x + 1.578947369 = 1.14405606 Simplifying x + 1.578947369 = 1.14405606 Reorder the terms: 1.578947369 + x = 1.14405606 Solving 1.578947369 + x = 1.14405606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.578947369' to each side of the equation. 1.578947369 + -1.578947369 + x = 1.14405606 + -1.578947369 Combine like terms: 1.578947369 + -1.578947369 = 0.000000000 0.000000000 + x = 1.14405606 + -1.578947369 x = 1.14405606 + -1.578947369 Combine like terms: 1.14405606 + -1.578947369 = -0.434891309 x = -0.434891309 Simplifying x = -0.434891309Subproblem 2
x + 1.578947369 = -1.14405606 Simplifying x + 1.578947369 = -1.14405606 Reorder the terms: 1.578947369 + x = -1.14405606 Solving 1.578947369 + x = -1.14405606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.578947369' to each side of the equation. 1.578947369 + -1.578947369 + x = -1.14405606 + -1.578947369 Combine like terms: 1.578947369 + -1.578947369 = 0.000000000 0.000000000 + x = -1.14405606 + -1.578947369 x = -1.14405606 + -1.578947369 Combine like terms: -1.14405606 + -1.578947369 = -2.723003429 x = -2.723003429 Simplifying x = -2.723003429Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.434891309, -2.723003429}
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