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Simplifying 2x2 + -9x + -736 = 0 Reorder the terms: -736 + -9x + 2x2 = 0 Solving -736 + -9x + 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'. -368 + -4.5x + x2 = 0 Move the constant term to the right: Add '368' to each side of the equation. -368 + -4.5x + 368 + x2 = 0 + 368 Reorder the terms: -368 + 368 + -4.5x + x2 = 0 + 368 Combine like terms: -368 + 368 = 0 0 + -4.5x + x2 = 0 + 368 -4.5x + x2 = 0 + 368 Combine like terms: 0 + 368 = 368 -4.5x + x2 = 368 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 368 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 368 + 5.0625 Combine like terms: 368 + 5.0625 = 373.0625 5.0625 + -4.5x + x2 = 373.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 373.0625 Calculate the square root of the right side: 19.314825912 Break this problem into two subproblems by setting (x + -2.25) equal to 19.314825912 and -19.314825912.Subproblem 1
x + -2.25 = 19.314825912 Simplifying x + -2.25 = 19.314825912 Reorder the terms: -2.25 + x = 19.314825912 Solving -2.25 + x = 19.314825912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 19.314825912 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 19.314825912 + 2.25 x = 19.314825912 + 2.25 Combine like terms: 19.314825912 + 2.25 = 21.564825912 x = 21.564825912 Simplifying x = 21.564825912Subproblem 2
x + -2.25 = -19.314825912 Simplifying x + -2.25 = -19.314825912 Reorder the terms: -2.25 + x = -19.314825912 Solving -2.25 + x = -19.314825912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -19.314825912 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -19.314825912 + 2.25 x = -19.314825912 + 2.25 Combine like terms: -19.314825912 + 2.25 = -17.064825912 x = -17.064825912 Simplifying x = -17.064825912Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.564825912, -17.064825912}
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