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Simplifying 18 + -2x = x2 + -5 Reorder the terms: 18 + -2x = -5 + x2 Solving 18 + -2x = -5 + x2 Solving for variable 'x'. Reorder the terms: 18 + 5 + -2x + -1x2 = -5 + x2 + 5 + -1x2 Combine like terms: 18 + 5 = 23 23 + -2x + -1x2 = -5 + x2 + 5 + -1x2 Reorder the terms: 23 + -2x + -1x2 = -5 + 5 + x2 + -1x2 Combine like terms: -5 + 5 = 0 23 + -2x + -1x2 = 0 + x2 + -1x2 23 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23 + 2x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 2x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 2x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 2x + x2 = 0 + 23 2x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 2x + x2 = 23 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 = 23 + 1 Reorder the terms: 1 + 2x + x2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + 2x + x2 = 24 Factor a perfect square on the left side: (x + 1)(x + 1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 1) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 1 = 4.898979486 Simplifying x + 1 = 4.898979486 Reorder the terms: 1 + x = 4.898979486 Solving 1 + x = 4.898979486 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 = 4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.898979486 + -1 x = 4.898979486 + -1 Combine like terms: 4.898979486 + -1 = 3.898979486 x = 3.898979486 Simplifying x = 3.898979486Subproblem 2
x + 1 = -4.898979486 Simplifying x + 1 = -4.898979486 Reorder the terms: 1 + x = -4.898979486 Solving 1 + x = -4.898979486 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 = -4.898979486 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.898979486 + -1 x = -4.898979486 + -1 Combine like terms: -4.898979486 + -1 = -5.898979486 x = -5.898979486 Simplifying x = -5.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.898979486, -5.898979486}
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