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Simplifying x2 + -1x = 2.8 Reorder the terms: -1x + x2 = 2.8 Solving -1x + x2 = 2.8 Solving for variable 'x'. Reorder the terms: -2.8 + -1x + x2 = 2.8 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 -2.8 + -1x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -1x + 2.8 + x2 = 0.0 + 2.8 Reorder the terms: -2.8 + 2.8 + -1x + x2 = 0.0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -1x + x2 = 0.0 + 2.8 -1x + x2 = 0.0 + 2.8 Combine like terms: 0.0 + 2.8 = 2.8 -1x + x2 = 2.8 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 = 2.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.8 + 0.25 Combine like terms: 2.8 + 0.25 = 3.05 0.25 + -1x + x2 = 3.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (x + -0.5) equal to 1.74642492 and -1.74642492.Subproblem 1
x + -0.5 = 1.74642492 Simplifying x + -0.5 = 1.74642492 Reorder the terms: -0.5 + x = 1.74642492 Solving -0.5 + x = 1.74642492 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 = 1.74642492 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.74642492 + 0.5 x = 1.74642492 + 0.5 Combine like terms: 1.74642492 + 0.5 = 2.24642492 x = 2.24642492 Simplifying x = 2.24642492Subproblem 2
x + -0.5 = -1.74642492 Simplifying x + -0.5 = -1.74642492 Reorder the terms: -0.5 + x = -1.74642492 Solving -0.5 + x = -1.74642492 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 = -1.74642492 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.74642492 + 0.5 x = -1.74642492 + 0.5 Combine like terms: -1.74642492 + 0.5 = -1.24642492 x = -1.24642492 Simplifying x = -1.24642492Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.24642492, -1.24642492}
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