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Simplifying x2 + 2x + -17.2 = 0 Reorder the terms: -17.2 + 2x + x2 = 0 Solving -17.2 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17.2' to each side of the equation. -17.2 + 2x + 17.2 + x2 = 0 + 17.2 Reorder the terms: -17.2 + 17.2 + 2x + x2 = 0 + 17.2 Combine like terms: -17.2 + 17.2 = 0.0 0.0 + 2x + x2 = 0 + 17.2 2x + x2 = 0 + 17.2 Combine like terms: 0 + 17.2 = 17.2 2x + x2 = 17.2 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 = 17.2 + 1 Reorder the terms: 1 + 2x + x2 = 17.2 + 1 Combine like terms: 17.2 + 1 = 18.2 1 + 2x + x2 = 18.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 18.2 Calculate the square root of the right side: 4.266145802 Break this problem into two subproblems by setting (x + 1) equal to 4.266145802 and -4.266145802.Subproblem 1
x + 1 = 4.266145802 Simplifying x + 1 = 4.266145802 Reorder the terms: 1 + x = 4.266145802 Solving 1 + x = 4.266145802 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 = 4.266145802 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.266145802 + -1 x = 4.266145802 + -1 Combine like terms: 4.266145802 + -1 = 3.266145802 x = 3.266145802 Simplifying x = 3.266145802Subproblem 2
x + 1 = -4.266145802 Simplifying x + 1 = -4.266145802 Reorder the terms: 1 + x = -4.266145802 Solving 1 + x = -4.266145802 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 = -4.266145802 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.266145802 + -1 x = -4.266145802 + -1 Combine like terms: -4.266145802 + -1 = -5.266145802 x = -5.266145802 Simplifying x = -5.266145802Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.266145802, -5.266145802}
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