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Simplifying 9x2 + -76x + -1144 = 0 Reorder the terms: -1144 + -76x + 9x2 = 0 Solving -1144 + -76x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -127.1111111 + -8.444444444x + x2 = 0 Move the constant term to the right: Add '127.1111111' to each side of the equation. -127.1111111 + -8.444444444x + 127.1111111 + x2 = 0 + 127.1111111 Reorder the terms: -127.1111111 + 127.1111111 + -8.444444444x + x2 = 0 + 127.1111111 Combine like terms: -127.1111111 + 127.1111111 = 0.0000000 0.0000000 + -8.444444444x + x2 = 0 + 127.1111111 -8.444444444x + x2 = 0 + 127.1111111 Combine like terms: 0 + 127.1111111 = 127.1111111 -8.444444444x + x2 = 127.1111111 The x term is -8.444444444x. Take half its coefficient (-4.222222222). Square it (17.82716049) and add it to both sides. Add '17.82716049' to each side of the equation. -8.444444444x + 17.82716049 + x2 = 127.1111111 + 17.82716049 Reorder the terms: 17.82716049 + -8.444444444x + x2 = 127.1111111 + 17.82716049 Combine like terms: 127.1111111 + 17.82716049 = 144.93827159 17.82716049 + -8.444444444x + x2 = 144.93827159 Factor a perfect square on the left side: (x + -4.222222222)(x + -4.222222222) = 144.93827159 Calculate the square root of the right side: 12.039031173 Break this problem into two subproblems by setting (x + -4.222222222) equal to 12.039031173 and -12.039031173.Subproblem 1
x + -4.222222222 = 12.039031173 Simplifying x + -4.222222222 = 12.039031173 Reorder the terms: -4.222222222 + x = 12.039031173 Solving -4.222222222 + x = 12.039031173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.222222222' to each side of the equation. -4.222222222 + 4.222222222 + x = 12.039031173 + 4.222222222 Combine like terms: -4.222222222 + 4.222222222 = 0.000000000 0.000000000 + x = 12.039031173 + 4.222222222 x = 12.039031173 + 4.222222222 Combine like terms: 12.039031173 + 4.222222222 = 16.261253395 x = 16.261253395 Simplifying x = 16.261253395Subproblem 2
x + -4.222222222 = -12.039031173 Simplifying x + -4.222222222 = -12.039031173 Reorder the terms: -4.222222222 + x = -12.039031173 Solving -4.222222222 + x = -12.039031173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.222222222' to each side of the equation. -4.222222222 + 4.222222222 + x = -12.039031173 + 4.222222222 Combine like terms: -4.222222222 + 4.222222222 = 0.000000000 0.000000000 + x = -12.039031173 + 4.222222222 x = -12.039031173 + 4.222222222 Combine like terms: -12.039031173 + 4.222222222 = -7.816808951 x = -7.816808951 Simplifying x = -7.816808951Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.261253395, -7.816808951}
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