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Simplifying 2x2 + -23x + -72 = 0 Reorder the terms: -72 + -23x + 2x2 = 0 Solving -72 + -23x + 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'. -36 + -11.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -11.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -11.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -11.5x + x2 = 0 + 36 -11.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -11.5x + x2 = 36 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 36 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 36 + 33.0625 Combine like terms: 36 + 33.0625 = 69.0625 33.0625 + -11.5x + x2 = 69.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 69.0625 Calculate the square root of the right side: 8.310385069 Break this problem into two subproblems by setting (x + -5.75) equal to 8.310385069 and -8.310385069.Subproblem 1
x + -5.75 = 8.310385069 Simplifying x + -5.75 = 8.310385069 Reorder the terms: -5.75 + x = 8.310385069 Solving -5.75 + x = 8.310385069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 8.310385069 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 8.310385069 + 5.75 x = 8.310385069 + 5.75 Combine like terms: 8.310385069 + 5.75 = 14.060385069 x = 14.060385069 Simplifying x = 14.060385069Subproblem 2
x + -5.75 = -8.310385069 Simplifying x + -5.75 = -8.310385069 Reorder the terms: -5.75 + x = -8.310385069 Solving -5.75 + x = -8.310385069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -8.310385069 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -8.310385069 + 5.75 x = -8.310385069 + 5.75 Combine like terms: -8.310385069 + 5.75 = -2.560385069 x = -2.560385069 Simplifying x = -2.560385069Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.060385069, -2.560385069}
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