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Simplifying 2x2 + -3x + -336 = 0 Reorder the terms: -336 + -3x + 2x2 = 0 Solving -336 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -168 + -1.5x + x2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -1.5x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -1.5x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -1.5x + x2 = 0 + 168 -1.5x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -1.5x + x2 = 168 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 168 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 168 + 0.5625 Combine like terms: 168 + 0.5625 = 168.5625 0.5625 + -1.5x + x2 = 168.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 168.5625 Calculate the square root of the right side: 12.983162173 Break this problem into two subproblems by setting (x + -0.75) equal to 12.983162173 and -12.983162173.Subproblem 1
x + -0.75 = 12.983162173 Simplifying x + -0.75 = 12.983162173 Reorder the terms: -0.75 + x = 12.983162173 Solving -0.75 + x = 12.983162173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 12.983162173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 12.983162173 + 0.75 x = 12.983162173 + 0.75 Combine like terms: 12.983162173 + 0.75 = 13.733162173 x = 13.733162173 Simplifying x = 13.733162173Subproblem 2
x + -0.75 = -12.983162173 Simplifying x + -0.75 = -12.983162173 Reorder the terms: -0.75 + x = -12.983162173 Solving -0.75 + x = -12.983162173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -12.983162173 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -12.983162173 + 0.75 x = -12.983162173 + 0.75 Combine like terms: -12.983162173 + 0.75 = -12.233162173 x = -12.233162173 Simplifying x = -12.233162173Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.733162173, -12.233162173}
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