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Simplifying 270 + 39x + 0.3x2 = 0 Solving 270 + 39x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 900 + 130x + x2 = 0 Move the constant term to the right: Add '-900' to each side of the equation. 900 + 130x + -900 + x2 = 0 + -900 Reorder the terms: 900 + -900 + 130x + x2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + 130x + x2 = 0 + -900 130x + x2 = 0 + -900 Combine like terms: 0 + -900 = -900 130x + x2 = -900 The x term is 130x. Take half its coefficient (65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. 130x + 4225 + x2 = -900 + 4225 Reorder the terms: 4225 + 130x + x2 = -900 + 4225 Combine like terms: -900 + 4225 = 3325 4225 + 130x + x2 = 3325 Factor a perfect square on the left side: (x + 65)(x + 65) = 3325 Calculate the square root of the right side: 57.662812973 Break this problem into two subproblems by setting (x + 65) equal to 57.662812973 and -57.662812973.Subproblem 1
x + 65 = 57.662812973 Simplifying x + 65 = 57.662812973 Reorder the terms: 65 + x = 57.662812973 Solving 65 + x = 57.662812973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = 57.662812973 + -65 Combine like terms: 65 + -65 = 0 0 + x = 57.662812973 + -65 x = 57.662812973 + -65 Combine like terms: 57.662812973 + -65 = -7.337187027 x = -7.337187027 Simplifying x = -7.337187027Subproblem 2
x + 65 = -57.662812973 Simplifying x + 65 = -57.662812973 Reorder the terms: 65 + x = -57.662812973 Solving 65 + x = -57.662812973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = -57.662812973 + -65 Combine like terms: 65 + -65 = 0 0 + x = -57.662812973 + -65 x = -57.662812973 + -65 Combine like terms: -57.662812973 + -65 = -122.662812973 x = -122.662812973 Simplifying x = -122.662812973Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.337187027, -122.662812973}
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