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Simplifying x2 + 6 + 36 + -1x = 90 Reorder the terms: 6 + 36 + -1x + x2 = 90 Combine like terms: 6 + 36 = 42 42 + -1x + x2 = 90 Solving 42 + -1x + x2 = 90 Solving for variable 'x'. Reorder the terms: 42 + -90 + -1x + x2 = 90 + -90 Combine like terms: 42 + -90 = -48 -48 + -1x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -48 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -1x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -1x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -1x + x2 = 0 + 48 -1x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -1x + x2 = 48 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 = 48 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 48 + 0.25 Combine like terms: 48 + 0.25 = 48.25 0.25 + -1x + x2 = 48.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -0.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -0.5 = 6.946221995 Simplifying x + -0.5 = 6.946221995 Reorder the terms: -0.5 + x = 6.946221995 Solving -0.5 + x = 6.946221995 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 = 6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.946221995 + 0.5 x = 6.946221995 + 0.5 Combine like terms: 6.946221995 + 0.5 = 7.446221995 x = 7.446221995 Simplifying x = 7.446221995Subproblem 2
x + -0.5 = -6.946221995 Simplifying x + -0.5 = -6.946221995 Reorder the terms: -0.5 + x = -6.946221995 Solving -0.5 + x = -6.946221995 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 = -6.946221995 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.946221995 + 0.5 x = -6.946221995 + 0.5 Combine like terms: -6.946221995 + 0.5 = -6.446221995 x = -6.446221995 Simplifying x = -6.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.446221995, -6.446221995}
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