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Simplifying X2 + -1X = 52 Reorder the terms: -1X + X2 = 52 Solving -1X + X2 = 52 Solving for variable 'X'. Reorder the terms: -52 + -1X + X2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -1X + 52 + X2 = 0 + 52 Reorder the terms: -52 + 52 + -1X + X2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -1X + X2 = 0 + 52 -1X + X2 = 0 + 52 Combine like terms: 0 + 52 = 52 -1X + X2 = 52 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 52 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 52 + 0.25 Combine like terms: 52 + 0.25 = 52.25 0.25 + -1X + X2 = 52.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (X + -0.5) equal to 7.228416147 and -7.228416147.Subproblem 1
X + -0.5 = 7.228416147 Simplifying X + -0.5 = 7.228416147 Reorder the terms: -0.5 + X = 7.228416147 Solving -0.5 + X = 7.228416147 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 7.228416147 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 7.228416147 + 0.5 X = 7.228416147 + 0.5 Combine like terms: 7.228416147 + 0.5 = 7.728416147 X = 7.728416147 Simplifying X = 7.728416147Subproblem 2
X + -0.5 = -7.228416147 Simplifying X + -0.5 = -7.228416147 Reorder the terms: -0.5 + X = -7.228416147 Solving -0.5 + X = -7.228416147 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -7.228416147 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -7.228416147 + 0.5 X = -7.228416147 + 0.5 Combine like terms: -7.228416147 + 0.5 = -6.728416147 X = -6.728416147 Simplifying X = -6.728416147Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.728416147, -6.728416147}
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