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Simplifying 21x2 + -97x + 63 = 0 Reorder the terms: 63 + -97x + 21x2 = 0 Solving 63 + -97x + 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 + -4.619047619x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.619047619x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.619047619x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.619047619x + x2 = 0 + -3 -4.619047619x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.619047619x + x2 = -3 The x term is -4.619047619x. Take half its coefficient (-2.30952381). Square it (5.333900229) and add it to both sides. Add '5.333900229' to each side of the equation. -4.619047619x + 5.333900229 + x2 = -3 + 5.333900229 Reorder the terms: 5.333900229 + -4.619047619x + x2 = -3 + 5.333900229 Combine like terms: -3 + 5.333900229 = 2.333900229 5.333900229 + -4.619047619x + x2 = 2.333900229 Factor a perfect square on the left side: (x + -2.30952381)(x + -2.30952381) = 2.333900229 Calculate the square root of the right side: 1.527710781 Break this problem into two subproblems by setting (x + -2.30952381) equal to 1.527710781 and -1.527710781.Subproblem 1
x + -2.30952381 = 1.527710781 Simplifying x + -2.30952381 = 1.527710781 Reorder the terms: -2.30952381 + x = 1.527710781 Solving -2.30952381 + x = 1.527710781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.30952381' to each side of the equation. -2.30952381 + 2.30952381 + x = 1.527710781 + 2.30952381 Combine like terms: -2.30952381 + 2.30952381 = 0.00000000 0.00000000 + x = 1.527710781 + 2.30952381 x = 1.527710781 + 2.30952381 Combine like terms: 1.527710781 + 2.30952381 = 3.837234591 x = 3.837234591 Simplifying x = 3.837234591Subproblem 2
x + -2.30952381 = -1.527710781 Simplifying x + -2.30952381 = -1.527710781 Reorder the terms: -2.30952381 + x = -1.527710781 Solving -2.30952381 + x = -1.527710781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.30952381' to each side of the equation. -2.30952381 + 2.30952381 + x = -1.527710781 + 2.30952381 Combine like terms: -2.30952381 + 2.30952381 = 0.00000000 0.00000000 + x = -1.527710781 + 2.30952381 x = -1.527710781 + 2.30952381 Combine like terms: -1.527710781 + 2.30952381 = 0.781813029 x = 0.781813029 Simplifying x = 0.781813029Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.837234591, 0.781813029}
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