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Simplifying 2x2 + -43x + -243 = 0 Reorder the terms: -243 + -43x + 2x2 = 0 Solving -243 + -43x + 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'. -121.5 + -21.5x + x2 = 0 Move the constant term to the right: Add '121.5' to each side of the equation. -121.5 + -21.5x + 121.5 + x2 = 0 + 121.5 Reorder the terms: -121.5 + 121.5 + -21.5x + x2 = 0 + 121.5 Combine like terms: -121.5 + 121.5 = 0.0 0.0 + -21.5x + x2 = 0 + 121.5 -21.5x + x2 = 0 + 121.5 Combine like terms: 0 + 121.5 = 121.5 -21.5x + x2 = 121.5 The x term is -21.5x. Take half its coefficient (-10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. -21.5x + 115.5625 + x2 = 121.5 + 115.5625 Reorder the terms: 115.5625 + -21.5x + x2 = 121.5 + 115.5625 Combine like terms: 121.5 + 115.5625 = 237.0625 115.5625 + -21.5x + x2 = 237.0625 Factor a perfect square on the left side: (x + -10.75)(x + -10.75) = 237.0625 Calculate the square root of the right side: 15.39683409 Break this problem into two subproblems by setting (x + -10.75) equal to 15.39683409 and -15.39683409.Subproblem 1
x + -10.75 = 15.39683409 Simplifying x + -10.75 = 15.39683409 Reorder the terms: -10.75 + x = 15.39683409 Solving -10.75 + x = 15.39683409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = 15.39683409 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = 15.39683409 + 10.75 x = 15.39683409 + 10.75 Combine like terms: 15.39683409 + 10.75 = 26.14683409 x = 26.14683409 Simplifying x = 26.14683409Subproblem 2
x + -10.75 = -15.39683409 Simplifying x + -10.75 = -15.39683409 Reorder the terms: -10.75 + x = -15.39683409 Solving -10.75 + x = -15.39683409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.75' to each side of the equation. -10.75 + 10.75 + x = -15.39683409 + 10.75 Combine like terms: -10.75 + 10.75 = 0.00 0.00 + x = -15.39683409 + 10.75 x = -15.39683409 + 10.75 Combine like terms: -15.39683409 + 10.75 = -4.64683409 x = -4.64683409 Simplifying x = -4.64683409Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.14683409, -4.64683409}
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