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Simplifying 850 = x2 + 2x + 300 Reorder the terms: 850 = 300 + 2x + x2 Solving 850 = 300 + 2x + x2 Solving for variable 'x'. Combine like terms: 850 + -300 = 550 550 + -2x + -1x2 = 300 + 2x + x2 + -300 + -2x + -1x2 Reorder the terms: 550 + -2x + -1x2 = 300 + -300 + 2x + -2x + x2 + -1x2 Combine like terms: 300 + -300 = 0 550 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 550 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 550 + -2x + -1x2 = 0 + x2 + -1x2 550 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 550 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -550 + 2x + x2 = 0 Move the constant term to the right: Add '550' to each side of the equation. -550 + 2x + 550 + x2 = 0 + 550 Reorder the terms: -550 + 550 + 2x + x2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + 2x + x2 = 0 + 550 2x + x2 = 0 + 550 Combine like terms: 0 + 550 = 550 2x + x2 = 550 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 550 + 1 Reorder the terms: 1 + 2x + x2 = 550 + 1 Combine like terms: 550 + 1 = 551 1 + 2x + x2 = 551 Factor a perfect square on the left side: (x + 1)(x + 1) = 551 Calculate the square root of the right side: 23.473389189 Break this problem into two subproblems by setting (x + 1) equal to 23.473389189 and -23.473389189.Subproblem 1
x + 1 = 23.473389189 Simplifying x + 1 = 23.473389189 Reorder the terms: 1 + x = 23.473389189 Solving 1 + x = 23.473389189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 23.473389189 + -1 Combine like terms: 1 + -1 = 0 0 + x = 23.473389189 + -1 x = 23.473389189 + -1 Combine like terms: 23.473389189 + -1 = 22.473389189 x = 22.473389189 Simplifying x = 22.473389189Subproblem 2
x + 1 = -23.473389189 Simplifying x + 1 = -23.473389189 Reorder the terms: 1 + x = -23.473389189 Solving 1 + x = -23.473389189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -23.473389189 + -1 Combine like terms: 1 + -1 = 0 0 + x = -23.473389189 + -1 x = -23.473389189 + -1 Combine like terms: -23.473389189 + -1 = -24.473389189 x = -24.473389189 Simplifying x = -24.473389189Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.473389189, -24.473389189}
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