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Simplifying 2x2 + -10x + -65 = 0 Reorder the terms: -65 + -10x + 2x2 = 0 Solving -65 + -10x + 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'. -32.5 + -5x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + -5x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + -5x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + -5x + x2 = 0 + 32.5 -5x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 -5x + x2 = 32.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 32.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 32.5 + 6.25 Combine like terms: 32.5 + 6.25 = 38.75 6.25 + -5x + x2 = 38.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 38.75 Calculate the square root of the right side: 6.224949799 Break this problem into two subproblems by setting (x + -2.5) equal to 6.224949799 and -6.224949799.Subproblem 1
x + -2.5 = 6.224949799 Simplifying x + -2.5 = 6.224949799 Reorder the terms: -2.5 + x = 6.224949799 Solving -2.5 + x = 6.224949799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.224949799 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.224949799 + 2.5 x = 6.224949799 + 2.5 Combine like terms: 6.224949799 + 2.5 = 8.724949799 x = 8.724949799 Simplifying x = 8.724949799Subproblem 2
x + -2.5 = -6.224949799 Simplifying x + -2.5 = -6.224949799 Reorder the terms: -2.5 + x = -6.224949799 Solving -2.5 + x = -6.224949799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.224949799 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.224949799 + 2.5 x = -6.224949799 + 2.5 Combine like terms: -6.224949799 + 2.5 = -3.724949799 x = -3.724949799 Simplifying x = -3.724949799Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.724949799, -3.724949799}
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