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Simplifying 2x2 + -48x + -69 = 0 Reorder the terms: -69 + -48x + 2x2 = 0 Solving -69 + -48x + 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'. -34.5 + -24x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + -24x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + -24x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + -24x + x2 = 0 + 34.5 -24x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 -24x + x2 = 34.5 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 34.5 + 144 Reorder the terms: 144 + -24x + x2 = 34.5 + 144 Combine like terms: 34.5 + 144 = 178.5 144 + -24x + x2 = 178.5 Factor a perfect square on the left side: (x + -12)(x + -12) = 178.5 Calculate the square root of the right side: 13.360389216 Break this problem into two subproblems by setting (x + -12) equal to 13.360389216 and -13.360389216.Subproblem 1
x + -12 = 13.360389216 Simplifying x + -12 = 13.360389216 Reorder the terms: -12 + x = 13.360389216 Solving -12 + x = 13.360389216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 13.360389216 + 12 Combine like terms: -12 + 12 = 0 0 + x = 13.360389216 + 12 x = 13.360389216 + 12 Combine like terms: 13.360389216 + 12 = 25.360389216 x = 25.360389216 Simplifying x = 25.360389216Subproblem 2
x + -12 = -13.360389216 Simplifying x + -12 = -13.360389216 Reorder the terms: -12 + x = -13.360389216 Solving -12 + x = -13.360389216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -13.360389216 + 12 Combine like terms: -12 + 12 = 0 0 + x = -13.360389216 + 12 x = -13.360389216 + 12 Combine like terms: -13.360389216 + 12 = -1.360389216 x = -1.360389216 Simplifying x = -1.360389216Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.360389216, -1.360389216}
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