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Simplifying X2 + 4X = 175 Reorder the terms: 4X + X2 = 175 Solving 4X + X2 = 175 Solving for variable 'X'. Reorder the terms: -175 + 4X + X2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 4X + 175 + X2 = 0 + 175 Reorder the terms: -175 + 175 + 4X + X2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 4X + X2 = 0 + 175 4X + X2 = 0 + 175 Combine like terms: 0 + 175 = 175 4X + X2 = 175 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 175 + 4 Reorder the terms: 4 + 4X + X2 = 175 + 4 Combine like terms: 175 + 4 = 179 4 + 4X + X2 = 179 Factor a perfect square on the left side: (X + 2)(X + 2) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (X + 2) equal to 13.37908816 and -13.37908816.Subproblem 1
X + 2 = 13.37908816 Simplifying X + 2 = 13.37908816 Reorder the terms: 2 + X = 13.37908816 Solving 2 + X = 13.37908816 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + X = 13.37908816 + -2 X = 13.37908816 + -2 Combine like terms: 13.37908816 + -2 = 11.37908816 X = 11.37908816 Simplifying X = 11.37908816Subproblem 2
X + 2 = -13.37908816 Simplifying X + 2 = -13.37908816 Reorder the terms: 2 + X = -13.37908816 Solving 2 + X = -13.37908816 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + X = -13.37908816 + -2 X = -13.37908816 + -2 Combine like terms: -13.37908816 + -2 = -15.37908816 X = -15.37908816 Simplifying X = -15.37908816Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.37908816, -15.37908816}
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