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Simplifying X2 + 4.8X + -5.76 = 0 Reorder the terms: -5.76 + 4.8X + X2 = 0 Solving -5.76 + 4.8X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '5.76' to each side of the equation. -5.76 + 4.8X + 5.76 + X2 = 0 + 5.76 Reorder the terms: -5.76 + 5.76 + 4.8X + X2 = 0 + 5.76 Combine like terms: -5.76 + 5.76 = 0.00 0.00 + 4.8X + X2 = 0 + 5.76 4.8X + X2 = 0 + 5.76 Combine like terms: 0 + 5.76 = 5.76 4.8X + X2 = 5.76 The X term is 4.8X. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8X + 5.76 + X2 = 5.76 + 5.76 Reorder the terms: 5.76 + 4.8X + X2 = 5.76 + 5.76 Combine like terms: 5.76 + 5.76 = 11.52 5.76 + 4.8X + X2 = 11.52 Factor a perfect square on the left side: (X + 2.4)(X + 2.4) = 11.52 Calculate the square root of the right side: 3.39411255 Break this problem into two subproblems by setting (X + 2.4) equal to 3.39411255 and -3.39411255.Subproblem 1
X + 2.4 = 3.39411255 Simplifying X + 2.4 = 3.39411255 Reorder the terms: 2.4 + X = 3.39411255 Solving 2.4 + X = 3.39411255 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + X = 3.39411255 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + X = 3.39411255 + -2.4 X = 3.39411255 + -2.4 Combine like terms: 3.39411255 + -2.4 = 0.99411255 X = 0.99411255 Simplifying X = 0.99411255Subproblem 2
X + 2.4 = -3.39411255 Simplifying X + 2.4 = -3.39411255 Reorder the terms: 2.4 + X = -3.39411255 Solving 2.4 + X = -3.39411255 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + X = -3.39411255 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + X = -3.39411255 + -2.4 X = -3.39411255 + -2.4 Combine like terms: -3.39411255 + -2.4 = -5.79411255 X = -5.79411255 Simplifying X = -5.79411255Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.99411255, -5.79411255}
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