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Simplifying 19200 = -27x2 + 1080x + 12312 Reorder the terms: 19200 = 12312 + 1080x + -27x2 Solving 19200 = 12312 + 1080x + -27x2 Solving for variable 'x'. Combine like terms: 19200 + -12312 = 6888 6888 + -1080x + 27x2 = 12312 + 1080x + -27x2 + -12312 + -1080x + 27x2 Reorder the terms: 6888 + -1080x + 27x2 = 12312 + -12312 + 1080x + -1080x + -27x2 + 27x2 Combine like terms: 12312 + -12312 = 0 6888 + -1080x + 27x2 = 0 + 1080x + -1080x + -27x2 + 27x2 6888 + -1080x + 27x2 = 1080x + -1080x + -27x2 + 27x2 Combine like terms: 1080x + -1080x = 0 6888 + -1080x + 27x2 = 0 + -27x2 + 27x2 6888 + -1080x + 27x2 = -27x2 + 27x2 Combine like terms: -27x2 + 27x2 = 0 6888 + -1080x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2296 + -360x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2296 + -360x + 9x2)' equal to zero and attempt to solve: Simplifying 2296 + -360x + 9x2 = 0 Solving 2296 + -360x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 255.1111111 + -40x + x2 = 0 Move the constant term to the right: Add '-255.1111111' to each side of the equation. 255.1111111 + -40x + -255.1111111 + x2 = 0 + -255.1111111 Reorder the terms: 255.1111111 + -255.1111111 + -40x + x2 = 0 + -255.1111111 Combine like terms: 255.1111111 + -255.1111111 = 0.0000000 0.0000000 + -40x + x2 = 0 + -255.1111111 -40x + x2 = 0 + -255.1111111 Combine like terms: 0 + -255.1111111 = -255.1111111 -40x + x2 = -255.1111111 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -255.1111111 + 400 Reorder the terms: 400 + -40x + x2 = -255.1111111 + 400 Combine like terms: -255.1111111 + 400 = 144.8888889 400 + -40x + x2 = 144.8888889 Factor a perfect square on the left side: (x + -20)(x + -20) = 144.8888889 Calculate the square root of the right side: 12.036980057 Break this problem into two subproblems by setting (x + -20) equal to 12.036980057 and -12.036980057.Subproblem 1
x + -20 = 12.036980057 Simplifying x + -20 = 12.036980057 Reorder the terms: -20 + x = 12.036980057 Solving -20 + x = 12.036980057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 12.036980057 + 20 Combine like terms: -20 + 20 = 0 0 + x = 12.036980057 + 20 x = 12.036980057 + 20 Combine like terms: 12.036980057 + 20 = 32.036980057 x = 32.036980057 Simplifying x = 32.036980057Subproblem 2
x + -20 = -12.036980057 Simplifying x + -20 = -12.036980057 Reorder the terms: -20 + x = -12.036980057 Solving -20 + x = -12.036980057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -12.036980057 + 20 Combine like terms: -20 + 20 = 0 0 + x = -12.036980057 + 20 x = -12.036980057 + 20 Combine like terms: -12.036980057 + 20 = 7.963019943 x = 7.963019943 Simplifying x = 7.963019943Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.036980057, 7.963019943}Solution
x = {32.036980057, 7.963019943}
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