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Simplifying 19 = x2 + -2x Reorder the terms: 19 = -2x + x2 Solving 19 = -2x + x2 Solving for variable 'x'. Reorder the terms: 19 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 19 + 2x + -1x2 = 0 + x2 + -1x2 19 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 19 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + -2x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -2x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -2x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2x + x2 = 0 + 19 -2x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2x + x2 = 19 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 = 19 + 1 Reorder the terms: 1 + -2x + x2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + -2x + x2 = 20 Factor a perfect square on the left side: (x + -1)(x + -1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -1) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -1 = 4.472135955 Simplifying x + -1 = 4.472135955 Reorder the terms: -1 + x = 4.472135955 Solving -1 + x = 4.472135955 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 = 4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.472135955 + 1 x = 4.472135955 + 1 Combine like terms: 4.472135955 + 1 = 5.472135955 x = 5.472135955 Simplifying x = 5.472135955Subproblem 2
x + -1 = -4.472135955 Simplifying x + -1 = -4.472135955 Reorder the terms: -1 + x = -4.472135955 Solving -1 + x = -4.472135955 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 = -4.472135955 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.472135955 + 1 x = -4.472135955 + 1 Combine like terms: -4.472135955 + 1 = -3.472135955 x = -3.472135955 Simplifying x = -3.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.472135955, -3.472135955}
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