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Simplifying x2 + -45x + 37.4 = 0 Reorder the terms: 37.4 + -45x + x2 = 0 Solving 37.4 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-37.4' to each side of the equation. 37.4 + -45x + -37.4 + x2 = 0 + -37.4 Reorder the terms: 37.4 + -37.4 + -45x + x2 = 0 + -37.4 Combine like terms: 37.4 + -37.4 = 0.0 0.0 + -45x + x2 = 0 + -37.4 -45x + x2 = 0 + -37.4 Combine like terms: 0 + -37.4 = -37.4 -45x + x2 = -37.4 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 = -37.4 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -37.4 + 506.25 Combine like terms: -37.4 + 506.25 = 468.85 506.25 + -45x + x2 = 468.85 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 468.85 Calculate the square root of the right side: 21.652944373 Break this problem into two subproblems by setting (x + -22.5) equal to 21.652944373 and -21.652944373.Subproblem 1
x + -22.5 = 21.652944373 Simplifying x + -22.5 = 21.652944373 Reorder the terms: -22.5 + x = 21.652944373 Solving -22.5 + x = 21.652944373 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 = 21.652944373 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 21.652944373 + 22.5 x = 21.652944373 + 22.5 Combine like terms: 21.652944373 + 22.5 = 44.152944373 x = 44.152944373 Simplifying x = 44.152944373Subproblem 2
x + -22.5 = -21.652944373 Simplifying x + -22.5 = -21.652944373 Reorder the terms: -22.5 + x = -21.652944373 Solving -22.5 + x = -21.652944373 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 = -21.652944373 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -21.652944373 + 22.5 x = -21.652944373 + 22.5 Combine like terms: -21.652944373 + 22.5 = 0.847055627 x = 0.847055627 Simplifying x = 0.847055627Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.152944373, 0.847055627}
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