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Simplifying X2 + -48X + 192 = 0 Reorder the terms: 192 + -48X + X2 = 0 Solving 192 + -48X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-192' to each side of the equation. 192 + -48X + -192 + X2 = 0 + -192 Reorder the terms: 192 + -192 + -48X + X2 = 0 + -192 Combine like terms: 192 + -192 = 0 0 + -48X + X2 = 0 + -192 -48X + X2 = 0 + -192 Combine like terms: 0 + -192 = -192 -48X + X2 = -192 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 = -192 + 576 Reorder the terms: 576 + -48X + X2 = -192 + 576 Combine like terms: -192 + 576 = 384 576 + -48X + X2 = 384 Factor a perfect square on the left side: (X + -24)(X + -24) = 384 Calculate the square root of the right side: 19.595917942 Break this problem into two subproblems by setting (X + -24) equal to 19.595917942 and -19.595917942.Subproblem 1
X + -24 = 19.595917942 Simplifying X + -24 = 19.595917942 Reorder the terms: -24 + X = 19.595917942 Solving -24 + X = 19.595917942 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 = 19.595917942 + 24 Combine like terms: -24 + 24 = 0 0 + X = 19.595917942 + 24 X = 19.595917942 + 24 Combine like terms: 19.595917942 + 24 = 43.595917942 X = 43.595917942 Simplifying X = 43.595917942Subproblem 2
X + -24 = -19.595917942 Simplifying X + -24 = -19.595917942 Reorder the terms: -24 + X = -19.595917942 Solving -24 + X = -19.595917942 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 = -19.595917942 + 24 Combine like terms: -24 + 24 = 0 0 + X = -19.595917942 + 24 X = -19.595917942 + 24 Combine like terms: -19.595917942 + 24 = 4.404082058 X = 4.404082058 Simplifying X = 4.404082058Solution
The solution to the problem is based on the solutions from the subproblems. X = {43.595917942, 4.404082058}
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