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Simplifying 45x + 6 = 5 + -1x2 Reorder the terms: 6 + 45x = 5 + -1x2 Solving 6 + 45x = 5 + -1x2 Solving for variable 'x'. Reorder the terms: 6 + -5 + 45x + x2 = 5 + -1x2 + -5 + x2 Combine like terms: 6 + -5 = 1 1 + 45x + x2 = 5 + -1x2 + -5 + x2 Reorder the terms: 1 + 45x + x2 = 5 + -5 + -1x2 + x2 Combine like terms: 5 + -5 = 0 1 + 45x + x2 = 0 + -1x2 + x2 1 + 45x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1 + 45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 45x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 45x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 45x + x2 = 0 + -1 45x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 45x + x2 = -1 The x term is 45x. Take half its coefficient (22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. 45x + 506.25 + x2 = -1 + 506.25 Reorder the terms: 506.25 + 45x + x2 = -1 + 506.25 Combine like terms: -1 + 506.25 = 505.25 506.25 + 45x + x2 = 505.25 Factor a perfect square on the left side: (x + 22.5)(x + 22.5) = 505.25 Calculate the square root of the right side: 22.477766793 Break this problem into two subproblems by setting (x + 22.5) equal to 22.477766793 and -22.477766793.Subproblem 1
x + 22.5 = 22.477766793 Simplifying x + 22.5 = 22.477766793 Reorder the terms: 22.5 + x = 22.477766793 Solving 22.5 + x = 22.477766793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = 22.477766793 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = 22.477766793 + -22.5 x = 22.477766793 + -22.5 Combine like terms: 22.477766793 + -22.5 = -0.022233207 x = -0.022233207 Simplifying x = -0.022233207Subproblem 2
x + 22.5 = -22.477766793 Simplifying x + 22.5 = -22.477766793 Reorder the terms: 22.5 + x = -22.477766793 Solving 22.5 + x = -22.477766793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.5' to each side of the equation. 22.5 + -22.5 + x = -22.477766793 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + x = -22.477766793 + -22.5 x = -22.477766793 + -22.5 Combine like terms: -22.477766793 + -22.5 = -44.977766793 x = -44.977766793 Simplifying x = -44.977766793Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.022233207, -44.977766793}
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