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Simplifying (1.5x * 1.5x) + 24x + 45 = 0 Reorder the terms for easier multiplication: (1.5 * 1.5x * x) + 24x + 45 = 0 Multiply 1.5 * 1.5 (2.25x * x) + 24x + 45 = 0 Multiply x * x (2.25x2) + 24x + 45 = 0 Reorder the terms: 45 + 24x + (2.25x2) = 0 Solving 45 + 24x + (2.25x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.25 the coefficient of the squared term: Divide each side by '2.25'. 20 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 10.66666667x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 10.66666667x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 10.66666667x + x2 = 0 + -20 10.66666667x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 10.66666667x + x2 = -20 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = -20 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = -20 + 28.44444446 Combine like terms: -20 + 28.44444446 = 8.44444446 28.44444446 + 10.66666667x + x2 = 8.44444446 Factor a perfect square on the left side: ((x) + 5.333333335)((x) + 5.333333335) = 8.44444446 Calculate the square root of the right side: 2.905932632 Break this problem into two subproblems by setting ((x) + 5.333333335) equal to 2.905932632 and -2.905932632.Subproblem 1
(x) + 5.333333335 = 2.905932632 Simplifying (x) + 5.333333335 = 2.905932632 x + 5.333333335 = 2.905932632 Reorder the terms: 5.333333335 + x = 2.905932632 Solving 5.333333335 + x = 2.905932632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 2.905932632 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 2.905932632 + -5.333333335 x = 2.905932632 + -5.333333335 Combine like terms: 2.905932632 + -5.333333335 = -2.427400703 x = -2.427400703 Simplifying x = -2.427400703Subproblem 2
(x) + 5.333333335 = -2.905932632 Simplifying (x) + 5.333333335 = -2.905932632 x + 5.333333335 = -2.905932632 Reorder the terms: 5.333333335 + x = -2.905932632 Solving 5.333333335 + x = -2.905932632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -2.905932632 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -2.905932632 + -5.333333335 x = -2.905932632 + -5.333333335 Combine like terms: -2.905932632 + -5.333333335 = -8.239265967 x = -8.239265967 Simplifying x = -8.239265967Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.427400703, -8.239265967}
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