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Simplifying x2 + -48x + 194 = 0 Reorder the terms: 194 + -48x + x2 = 0 Solving 194 + -48x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-194' to each side of the equation. 194 + -48x + -194 + x2 = 0 + -194 Reorder the terms: 194 + -194 + -48x + x2 = 0 + -194 Combine like terms: 194 + -194 = 0 0 + -48x + x2 = 0 + -194 -48x + x2 = 0 + -194 Combine like terms: 0 + -194 = -194 -48x + x2 = -194 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 = -194 + 576 Reorder the terms: 576 + -48x + x2 = -194 + 576 Combine like terms: -194 + 576 = 382 576 + -48x + x2 = 382 Factor a perfect square on the left side: (x + -24)(x + -24) = 382 Calculate the square root of the right side: 19.544820286 Break this problem into two subproblems by setting (x + -24) equal to 19.544820286 and -19.544820286.Subproblem 1
x + -24 = 19.544820286 Simplifying x + -24 = 19.544820286 Reorder the terms: -24 + x = 19.544820286 Solving -24 + x = 19.544820286 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 = 19.544820286 + 24 Combine like terms: -24 + 24 = 0 0 + x = 19.544820286 + 24 x = 19.544820286 + 24 Combine like terms: 19.544820286 + 24 = 43.544820286 x = 43.544820286 Simplifying x = 43.544820286Subproblem 2
x + -24 = -19.544820286 Simplifying x + -24 = -19.544820286 Reorder the terms: -24 + x = -19.544820286 Solving -24 + x = -19.544820286 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 = -19.544820286 + 24 Combine like terms: -24 + 24 = 0 0 + x = -19.544820286 + 24 x = -19.544820286 + 24 Combine like terms: -19.544820286 + 24 = 4.455179714 x = 4.455179714 Simplifying x = 4.455179714Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.544820286, 4.455179714}
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