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Simplifying (1x * 2x) + 24x + 45 = 0 Reorder the terms for easier multiplication: (1 * 2x * x) + 24x + 45 = 0 Multiply 1 * 2 (2x * x) + 24x + 45 = 0 Multiply x * x (2x2) + 24x + 45 = 0 Reorder the terms: 45 + 24x + (2x2) = 0 Solving 45 + 24x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 12x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 12x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 12x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 12x + x2 = 0 + -22.5 12x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 12x + x2 = -22.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -22.5 + 36 Reorder the terms: 36 + 12x + x2 = -22.5 + 36 Combine like terms: -22.5 + 36 = 13.5 36 + 12x + x2 = 13.5 Factor a perfect square on the left side: ((x) + 6)((x) + 6) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting ((x) + 6) equal to 3.674234614 and -3.674234614.Subproblem 1
(x) + 6 = 3.674234614 Simplifying (x) + 6 = 3.674234614 x + 6 = 3.674234614 Reorder the terms: 6 + x = 3.674234614 Solving 6 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 3.674234614 + -6 Combine like terms: 6 + -6 = 0 0 + x = 3.674234614 + -6 x = 3.674234614 + -6 Combine like terms: 3.674234614 + -6 = -2.325765386 x = -2.325765386 Simplifying x = -2.325765386Subproblem 2
(x) + 6 = -3.674234614 Simplifying (x) + 6 = -3.674234614 x + 6 = -3.674234614 Reorder the terms: 6 + x = -3.674234614 Solving 6 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -3.674234614 + -6 Combine like terms: 6 + -6 = 0 0 + x = -3.674234614 + -6 x = -3.674234614 + -6 Combine like terms: -3.674234614 + -6 = -9.674234614 x = -9.674234614 Simplifying x = -9.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.325765386, -9.674234614}
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