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Simplifying x2 + -1x + -46 = 0 Reorder the terms: -46 + -1x + x2 = 0 Solving -46 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -1x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -1x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -1x + x2 = 0 + 46 -1x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -1x + x2 = 46 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 = 46 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 46 + 0.25 Combine like terms: 46 + 0.25 = 46.25 0.25 + -1x + x2 = 46.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -0.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -0.5 = 6.800735254 Simplifying x + -0.5 = 6.800735254 Reorder the terms: -0.5 + x = 6.800735254 Solving -0.5 + x = 6.800735254 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 = 6.800735254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.800735254 + 0.5 x = 6.800735254 + 0.5 Combine like terms: 6.800735254 + 0.5 = 7.300735254 x = 7.300735254 Simplifying x = 7.300735254Subproblem 2
x + -0.5 = -6.800735254 Simplifying x + -0.5 = -6.800735254 Reorder the terms: -0.5 + x = -6.800735254 Solving -0.5 + x = -6.800735254 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 = -6.800735254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.800735254 + 0.5 x = -6.800735254 + 0.5 Combine like terms: -6.800735254 + 0.5 = -6.300735254 x = -6.300735254 Simplifying x = -6.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.300735254, -6.300735254}
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