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Simplifying 2x(x + 2) = 45 Reorder the terms: 2x(2 + x) = 45 (2 * 2x + x * 2x) = 45 (4x + 2x2) = 45 Solving 4x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 4x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + 2x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + 2x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + 2x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + 2x + x2 = 0 + 22.5 2x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 2x + x2 = 22.5 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 = 22.5 + 1 Reorder the terms: 1 + 2x + x2 = 22.5 + 1 Combine like terms: 22.5 + 1 = 23.5 1 + 2x + x2 = 23.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + 1) equal to 4.847679857 and -4.847679857.Subproblem 1
x + 1 = 4.847679857 Simplifying x + 1 = 4.847679857 Reorder the terms: 1 + x = 4.847679857 Solving 1 + x = 4.847679857 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 = 4.847679857 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.847679857 + -1 x = 4.847679857 + -1 Combine like terms: 4.847679857 + -1 = 3.847679857 x = 3.847679857 Simplifying x = 3.847679857Subproblem 2
x + 1 = -4.847679857 Simplifying x + 1 = -4.847679857 Reorder the terms: 1 + x = -4.847679857 Solving 1 + x = -4.847679857 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 = -4.847679857 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.847679857 + -1 x = -4.847679857 + -1 Combine like terms: -4.847679857 + -1 = -5.847679857 x = -5.847679857 Simplifying x = -5.847679857Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.847679857, -5.847679857}
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