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Simplifying x2 + -1x + -264 = 0 Reorder the terms: -264 + -1x + x2 = 0 Solving -264 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '264' to each side of the equation. -264 + -1x + 264 + x2 = 0 + 264 Reorder the terms: -264 + 264 + -1x + x2 = 0 + 264 Combine like terms: -264 + 264 = 0 0 + -1x + x2 = 0 + 264 -1x + x2 = 0 + 264 Combine like terms: 0 + 264 = 264 -1x + x2 = 264 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 = 264 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 264 + 0.25 Combine like terms: 264 + 0.25 = 264.25 0.25 + -1x + x2 = 264.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (x + -0.5) equal to 16.255768207 and -16.255768207.Subproblem 1
x + -0.5 = 16.255768207 Simplifying x + -0.5 = 16.255768207 Reorder the terms: -0.5 + x = 16.255768207 Solving -0.5 + x = 16.255768207 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 = 16.255768207 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 16.255768207 + 0.5 x = 16.255768207 + 0.5 Combine like terms: 16.255768207 + 0.5 = 16.755768207 x = 16.755768207 Simplifying x = 16.755768207Subproblem 2
x + -0.5 = -16.255768207 Simplifying x + -0.5 = -16.255768207 Reorder the terms: -0.5 + x = -16.255768207 Solving -0.5 + x = -16.255768207 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 = -16.255768207 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -16.255768207 + 0.5 x = -16.255768207 + 0.5 Combine like terms: -16.255768207 + 0.5 = -15.755768207 x = -15.755768207 Simplifying x = -15.755768207Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.755768207, -15.755768207}
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