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Simplifying x2 + 48x + -138 = 0 Reorder the terms: -138 + 48x + x2 = 0 Solving -138 + 48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 48x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 48x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 48x + x2 = 0 + 138 48x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 48x + x2 = 138 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = 138 + 576 Reorder the terms: 576 + 48x + x2 = 138 + 576 Combine like terms: 138 + 576 = 714 576 + 48x + x2 = 714 Factor a perfect square on the left side: (x + 24)(x + 24) = 714 Calculate the square root of the right side: 26.720778432 Break this problem into two subproblems by setting (x + 24) equal to 26.720778432 and -26.720778432.Subproblem 1
x + 24 = 26.720778432 Simplifying x + 24 = 26.720778432 Reorder the terms: 24 + x = 26.720778432 Solving 24 + x = 26.720778432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 26.720778432 + -24 Combine like terms: 24 + -24 = 0 0 + x = 26.720778432 + -24 x = 26.720778432 + -24 Combine like terms: 26.720778432 + -24 = 2.720778432 x = 2.720778432 Simplifying x = 2.720778432Subproblem 2
x + 24 = -26.720778432 Simplifying x + 24 = -26.720778432 Reorder the terms: 24 + x = -26.720778432 Solving 24 + x = -26.720778432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -26.720778432 + -24 Combine like terms: 24 + -24 = 0 0 + x = -26.720778432 + -24 x = -26.720778432 + -24 Combine like terms: -26.720778432 + -24 = -50.720778432 x = -50.720778432 Simplifying x = -50.720778432Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.720778432, -50.720778432}
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