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Simplifying 21x2 + -13x + -2 = 0 Reorder the terms: -2 + -13x + 21x2 = 0 Solving -2 + -13x + 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'. -0.09523809524 + -0.619047619x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + -0.619047619x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + -0.619047619x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + -0.619047619x + x2 = 0 + 0.09523809524 -0.619047619x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 -0.619047619x + x2 = 0.09523809524 The x term is -0.619047619x. Take half its coefficient (-0.3095238095). Square it (0.09580498865) and add it to both sides. Add '0.09580498865' to each side of the equation. -0.619047619x + 0.09580498865 + x2 = 0.09523809524 + 0.09580498865 Reorder the terms: 0.09580498865 + -0.619047619x + x2 = 0.09523809524 + 0.09580498865 Combine like terms: 0.09523809524 + 0.09580498865 = 0.19104308389 0.09580498865 + -0.619047619x + x2 = 0.19104308389 Factor a perfect square on the left side: (x + -0.3095238095)(x + -0.3095238095) = 0.19104308389 Calculate the square root of the right side: 0.437084756 Break this problem into two subproblems by setting (x + -0.3095238095) equal to 0.437084756 and -0.437084756.Subproblem 1
x + -0.3095238095 = 0.437084756 Simplifying x + -0.3095238095 = 0.437084756 Reorder the terms: -0.3095238095 + x = 0.437084756 Solving -0.3095238095 + x = 0.437084756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + x = 0.437084756 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + x = 0.437084756 + 0.3095238095 x = 0.437084756 + 0.3095238095 Combine like terms: 0.437084756 + 0.3095238095 = 0.7466085655 x = 0.7466085655 Simplifying x = 0.7466085655Subproblem 2
x + -0.3095238095 = -0.437084756 Simplifying x + -0.3095238095 = -0.437084756 Reorder the terms: -0.3095238095 + x = -0.437084756 Solving -0.3095238095 + x = -0.437084756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3095238095' to each side of the equation. -0.3095238095 + 0.3095238095 + x = -0.437084756 + 0.3095238095 Combine like terms: -0.3095238095 + 0.3095238095 = 0.0000000000 0.0000000000 + x = -0.437084756 + 0.3095238095 x = -0.437084756 + 0.3095238095 Combine like terms: -0.437084756 + 0.3095238095 = -0.1275609465 x = -0.1275609465 Simplifying x = -0.1275609465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7466085655, -0.1275609465}
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