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Simplifying x2 + -45.5x + 91 = 0 Reorder the terms: 91 + -45.5x + x2 = 0 Solving 91 + -45.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-91' to each side of the equation. 91 + -45.5x + -91 + x2 = 0 + -91 Reorder the terms: 91 + -91 + -45.5x + x2 = 0 + -91 Combine like terms: 91 + -91 = 0 0 + -45.5x + x2 = 0 + -91 -45.5x + x2 = 0 + -91 Combine like terms: 0 + -91 = -91 -45.5x + x2 = -91 The x term is -45.5x. Take half its coefficient (-22.75). Square it (517.5625) and add it to both sides. Add '517.5625' to each side of the equation. -45.5x + 517.5625 + x2 = -91 + 517.5625 Reorder the terms: 517.5625 + -45.5x + x2 = -91 + 517.5625 Combine like terms: -91 + 517.5625 = 426.5625 517.5625 + -45.5x + x2 = 426.5625 Factor a perfect square on the left side: (x + -22.75)(x + -22.75) = 426.5625 Calculate the square root of the right side: 20.653389552 Break this problem into two subproblems by setting (x + -22.75) equal to 20.653389552 and -20.653389552.Subproblem 1
x + -22.75 = 20.653389552 Simplifying x + -22.75 = 20.653389552 Reorder the terms: -22.75 + x = 20.653389552 Solving -22.75 + x = 20.653389552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.75' to each side of the equation. -22.75 + 22.75 + x = 20.653389552 + 22.75 Combine like terms: -22.75 + 22.75 = 0.00 0.00 + x = 20.653389552 + 22.75 x = 20.653389552 + 22.75 Combine like terms: 20.653389552 + 22.75 = 43.403389552 x = 43.403389552 Simplifying x = 43.403389552Subproblem 2
x + -22.75 = -20.653389552 Simplifying x + -22.75 = -20.653389552 Reorder the terms: -22.75 + x = -20.653389552 Solving -22.75 + x = -20.653389552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.75' to each side of the equation. -22.75 + 22.75 + x = -20.653389552 + 22.75 Combine like terms: -22.75 + 22.75 = 0.00 0.00 + x = -20.653389552 + 22.75 x = -20.653389552 + 22.75 Combine like terms: -20.653389552 + 22.75 = 2.096610448 x = 2.096610448 Simplifying x = 2.096610448Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.403389552, 2.096610448}
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