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Simplifying 21x2 + -55x + -64 = 0 Reorder the terms: -64 + -55x + 21x2 = 0 Solving -64 + -55x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -3.047619048 + -2.619047619x + x2 = 0 Move the constant term to the right: Add '3.047619048' to each side of the equation. -3.047619048 + -2.619047619x + 3.047619048 + x2 = 0 + 3.047619048 Reorder the terms: -3.047619048 + 3.047619048 + -2.619047619x + x2 = 0 + 3.047619048 Combine like terms: -3.047619048 + 3.047619048 = 0.000000000 0.000000000 + -2.619047619x + x2 = 0 + 3.047619048 -2.619047619x + x2 = 0 + 3.047619048 Combine like terms: 0 + 3.047619048 = 3.047619048 -2.619047619x + x2 = 3.047619048 The x term is -2.619047619x. Take half its coefficient (-1.30952381). Square it (1.714852609) and add it to both sides. Add '1.714852609' to each side of the equation. -2.619047619x + 1.714852609 + x2 = 3.047619048 + 1.714852609 Reorder the terms: 1.714852609 + -2.619047619x + x2 = 3.047619048 + 1.714852609 Combine like terms: 3.047619048 + 1.714852609 = 4.762471657 1.714852609 + -2.619047619x + x2 = 4.762471657 Factor a perfect square on the left side: (x + -1.30952381)(x + -1.30952381) = 4.762471657 Calculate the square root of the right side: 2.18230879 Break this problem into two subproblems by setting (x + -1.30952381) equal to 2.18230879 and -2.18230879.Subproblem 1
x + -1.30952381 = 2.18230879 Simplifying x + -1.30952381 = 2.18230879 Reorder the terms: -1.30952381 + x = 2.18230879 Solving -1.30952381 + x = 2.18230879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.30952381' to each side of the equation. -1.30952381 + 1.30952381 + x = 2.18230879 + 1.30952381 Combine like terms: -1.30952381 + 1.30952381 = 0.00000000 0.00000000 + x = 2.18230879 + 1.30952381 x = 2.18230879 + 1.30952381 Combine like terms: 2.18230879 + 1.30952381 = 3.4918326 x = 3.4918326 Simplifying x = 3.4918326Subproblem 2
x + -1.30952381 = -2.18230879 Simplifying x + -1.30952381 = -2.18230879 Reorder the terms: -1.30952381 + x = -2.18230879 Solving -1.30952381 + x = -2.18230879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.30952381' to each side of the equation. -1.30952381 + 1.30952381 + x = -2.18230879 + 1.30952381 Combine like terms: -1.30952381 + 1.30952381 = 0.00000000 0.00000000 + x = -2.18230879 + 1.30952381 x = -2.18230879 + 1.30952381 Combine like terms: -2.18230879 + 1.30952381 = -0.87278498 x = -0.87278498 Simplifying x = -0.87278498Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4918326, -0.87278498}
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