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Simplifying x2 + -45x + 43 = 0 Reorder the terms: 43 + -45x + x2 = 0 Solving 43 + -45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -45x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + -45x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -45x + x2 = 0 + -43 -45x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 -45x + x2 = -43 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 = -43 + 506.25 Reorder the terms: 506.25 + -45x + x2 = -43 + 506.25 Combine like terms: -43 + 506.25 = 463.25 506.25 + -45x + x2 = 463.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 463.25 Calculate the square root of the right side: 21.52324325 Break this problem into two subproblems by setting (x + -22.5) equal to 21.52324325 and -21.52324325.Subproblem 1
x + -22.5 = 21.52324325 Simplifying x + -22.5 = 21.52324325 Reorder the terms: -22.5 + x = 21.52324325 Solving -22.5 + x = 21.52324325 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 = 21.52324325 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 21.52324325 + 22.5 x = 21.52324325 + 22.5 Combine like terms: 21.52324325 + 22.5 = 44.02324325 x = 44.02324325 Simplifying x = 44.02324325Subproblem 2
x + -22.5 = -21.52324325 Simplifying x + -22.5 = -21.52324325 Reorder the terms: -22.5 + x = -21.52324325 Solving -22.5 + x = -21.52324325 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 = -21.52324325 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -21.52324325 + 22.5 x = -21.52324325 + 22.5 Combine like terms: -21.52324325 + 22.5 = 0.97675675 x = 0.97675675 Simplifying x = 0.97675675Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.02324325, 0.97675675}
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