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Simplifying x2 + -105x + 156 = 0 Reorder the terms: 156 + -105x + x2 = 0 Solving 156 + -105x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + -105x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + -105x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + -105x + x2 = 0 + -156 -105x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 -105x + x2 = -156 The x term is -105x. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105x + 2756.25 + x2 = -156 + 2756.25 Reorder the terms: 2756.25 + -105x + x2 = -156 + 2756.25 Combine like terms: -156 + 2756.25 = 2600.25 2756.25 + -105x + x2 = 2600.25 Factor a perfect square on the left side: (x + -52.5)(x + -52.5) = 2600.25 Calculate the square root of the right side: 50.992646529 Break this problem into two subproblems by setting (x + -52.5) equal to 50.992646529 and -50.992646529.Subproblem 1
x + -52.5 = 50.992646529 Simplifying x + -52.5 = 50.992646529 Reorder the terms: -52.5 + x = 50.992646529 Solving -52.5 + x = 50.992646529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = 50.992646529 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = 50.992646529 + 52.5 x = 50.992646529 + 52.5 Combine like terms: 50.992646529 + 52.5 = 103.492646529 x = 103.492646529 Simplifying x = 103.492646529Subproblem 2
x + -52.5 = -50.992646529 Simplifying x + -52.5 = -50.992646529 Reorder the terms: -52.5 + x = -50.992646529 Solving -52.5 + x = -50.992646529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = -50.992646529 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = -50.992646529 + 52.5 x = -50.992646529 + 52.5 Combine like terms: -50.992646529 + 52.5 = 1.507353471 x = 1.507353471 Simplifying x = 1.507353471Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.492646529, 1.507353471}
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