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Simplifying 54x + -0.3x2 = 10x + 15 Reorder the terms: 54x + -0.3x2 = 15 + 10x Solving 54x + -0.3x2 = 15 + 10x Solving for variable 'x'. Reorder the terms: -15 + 54x + -10x + -0.3x2 = 15 + 10x + -15 + -10x Combine like terms: 54x + -10x = 44x -15 + 44x + -0.3x2 = 15 + 10x + -15 + -10x Reorder the terms: -15 + 44x + -0.3x2 = 15 + -15 + 10x + -10x Combine like terms: 15 + -15 = 0 -15 + 44x + -0.3x2 = 0 + 10x + -10x -15 + 44x + -0.3x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -15 + 44x + -0.3x2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 50 + -146.6666667x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -146.6666667x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -146.6666667x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -146.6666667x + x2 = 0 + -50 -146.6666667x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -146.6666667x + x2 = -50 The x term is -146.6666667x. Take half its coefficient (-73.33333335). Square it (5377.777780) and add it to both sides. Add '5377.777780' to each side of the equation. -146.6666667x + 5377.777780 + x2 = -50 + 5377.777780 Reorder the terms: 5377.777780 + -146.6666667x + x2 = -50 + 5377.777780 Combine like terms: -50 + 5377.777780 = 5327.77778 5377.777780 + -146.6666667x + x2 = 5327.77778 Factor a perfect square on the left side: (x + -73.33333335)(x + -73.33333335) = 5327.77778 Calculate the square root of the right side: 72.99162815 Break this problem into two subproblems by setting (x + -73.33333335) equal to 72.99162815 and -72.99162815.Subproblem 1
x + -73.33333335 = 72.99162815 Simplifying x + -73.33333335 = 72.99162815 Reorder the terms: -73.33333335 + x = 72.99162815 Solving -73.33333335 + x = 72.99162815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73.33333335' to each side of the equation. -73.33333335 + 73.33333335 + x = 72.99162815 + 73.33333335 Combine like terms: -73.33333335 + 73.33333335 = 0.00000000 0.00000000 + x = 72.99162815 + 73.33333335 x = 72.99162815 + 73.33333335 Combine like terms: 72.99162815 + 73.33333335 = 146.3249615 x = 146.3249615 Simplifying x = 146.3249615Subproblem 2
x + -73.33333335 = -72.99162815 Simplifying x + -73.33333335 = -72.99162815 Reorder the terms: -73.33333335 + x = -72.99162815 Solving -73.33333335 + x = -72.99162815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '73.33333335' to each side of the equation. -73.33333335 + 73.33333335 + x = -72.99162815 + 73.33333335 Combine like terms: -73.33333335 + 73.33333335 = 0.00000000 0.00000000 + x = -72.99162815 + 73.33333335 x = -72.99162815 + 73.33333335 Combine like terms: -72.99162815 + 73.33333335 = 0.3417052 x = 0.3417052 Simplifying x = 0.3417052Solution
The solution to the problem is based on the solutions from the subproblems. x = {146.3249615, 0.3417052}
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