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Simplifying 2x2 + -7x + -64 = 0 Reorder the terms: -64 + -7x + 2x2 = 0 Solving -64 + -7x + 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 + -3.5x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -3.5x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -3.5x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -3.5x + x2 = 0 + 32 -3.5x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -3.5x + x2 = 32 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 32 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 32 + 3.0625 Combine like terms: 32 + 3.0625 = 35.0625 3.0625 + -3.5x + x2 = 35.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 35.0625 Calculate the square root of the right side: 5.921359641 Break this problem into two subproblems by setting (x + -1.75) equal to 5.921359641 and -5.921359641.Subproblem 1
x + -1.75 = 5.921359641 Simplifying x + -1.75 = 5.921359641 Reorder the terms: -1.75 + x = 5.921359641 Solving -1.75 + x = 5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 5.921359641 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 5.921359641 + 1.75 x = 5.921359641 + 1.75 Combine like terms: 5.921359641 + 1.75 = 7.671359641 x = 7.671359641 Simplifying x = 7.671359641Subproblem 2
x + -1.75 = -5.921359641 Simplifying x + -1.75 = -5.921359641 Reorder the terms: -1.75 + x = -5.921359641 Solving -1.75 + x = -5.921359641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -5.921359641 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -5.921359641 + 1.75 x = -5.921359641 + 1.75 Combine like terms: -5.921359641 + 1.75 = -4.171359641 x = -4.171359641 Simplifying x = -4.171359641Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.671359641, -4.171359641}
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