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Simplifying x * x + -54 = 13 + x Multiply x * x x2 + -54 = 13 + x Reorder the terms: -54 + x2 = 13 + x Solving -54 + x2 = 13 + x Solving for variable 'x'. Reorder the terms: -54 + -13 + -1x + x2 = 13 + x + -13 + -1x Combine like terms: -54 + -13 = -67 -67 + -1x + x2 = 13 + x + -13 + -1x Reorder the terms: -67 + -1x + x2 = 13 + -13 + x + -1x Combine like terms: 13 + -13 = 0 -67 + -1x + x2 = 0 + x + -1x -67 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -67 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + -1x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -1x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -1x + x2 = 0 + 67 -1x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -1x + x2 = 67 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 = 67 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 67 + 0.25 Combine like terms: 67 + 0.25 = 67.25 0.25 + -1x + x2 = 67.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + -0.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + -0.5 = 8.200609733 Simplifying x + -0.5 = 8.200609733 Reorder the terms: -0.5 + x = 8.200609733 Solving -0.5 + x = 8.200609733 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 = 8.200609733 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.200609733 + 0.5 x = 8.200609733 + 0.5 Combine like terms: 8.200609733 + 0.5 = 8.700609733 x = 8.700609733 Simplifying x = 8.700609733Subproblem 2
x + -0.5 = -8.200609733 Simplifying x + -0.5 = -8.200609733 Reorder the terms: -0.5 + x = -8.200609733 Solving -0.5 + x = -8.200609733 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 = -8.200609733 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.200609733 + 0.5 x = -8.200609733 + 0.5 Combine like terms: -8.200609733 + 0.5 = -7.700609733 x = -7.700609733 Simplifying x = -7.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.700609733, -7.700609733}
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