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Simplifying -3x2 + 108x + -970 = 0 Reorder the terms: -970 + 108x + -3x2 = 0 Solving -970 + 108x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 323.3333333 + -36x + x2 = 0 Move the constant term to the right: Add '-323.3333333' to each side of the equation. 323.3333333 + -36x + -323.3333333 + x2 = 0 + -323.3333333 Reorder the terms: 323.3333333 + -323.3333333 + -36x + x2 = 0 + -323.3333333 Combine like terms: 323.3333333 + -323.3333333 = 0.0000000 0.0000000 + -36x + x2 = 0 + -323.3333333 -36x + x2 = 0 + -323.3333333 Combine like terms: 0 + -323.3333333 = -323.3333333 -36x + x2 = -323.3333333 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -323.3333333 + 324 Reorder the terms: 324 + -36x + x2 = -323.3333333 + 324 Combine like terms: -323.3333333 + 324 = 0.6666667 324 + -36x + x2 = 0.6666667 Factor a perfect square on the left side: (x + -18)(x + -18) = 0.6666667 Calculate the square root of the right side: 0.816496601 Break this problem into two subproblems by setting (x + -18) equal to 0.816496601 and -0.816496601.Subproblem 1
x + -18 = 0.816496601 Simplifying x + -18 = 0.816496601 Reorder the terms: -18 + x = 0.816496601 Solving -18 + x = 0.816496601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 0.816496601 + 18 Combine like terms: -18 + 18 = 0 0 + x = 0.816496601 + 18 x = 0.816496601 + 18 Combine like terms: 0.816496601 + 18 = 18.816496601 x = 18.816496601 Simplifying x = 18.816496601Subproblem 2
x + -18 = -0.816496601 Simplifying x + -18 = -0.816496601 Reorder the terms: -18 + x = -0.816496601 Solving -18 + x = -0.816496601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -0.816496601 + 18 Combine like terms: -18 + 18 = 0 0 + x = -0.816496601 + 18 x = -0.816496601 + 18 Combine like terms: -0.816496601 + 18 = 17.183503399 x = 17.183503399 Simplifying x = 17.183503399Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.816496601, 17.183503399}
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