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Simplifying 21x2 + 56x + -16 = 0 Reorder the terms: -16 + 56x + 21x2 = 0 Solving -16 + 56x + 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'. -0.7619047619 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '0.7619047619' to each side of the equation. -0.7619047619 + 2.666666667x + 0.7619047619 + x2 = 0 + 0.7619047619 Reorder the terms: -0.7619047619 + 0.7619047619 + 2.666666667x + x2 = 0 + 0.7619047619 Combine like terms: -0.7619047619 + 0.7619047619 = 0.0000000000 0.0000000000 + 2.666666667x + x2 = 0 + 0.7619047619 2.666666667x + x2 = 0 + 0.7619047619 Combine like terms: 0 + 0.7619047619 = 0.7619047619 2.666666667x + x2 = 0.7619047619 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 0.7619047619 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 0.7619047619 + 1.777777780 Combine like terms: 0.7619047619 + 1.777777780 = 2.5396825419 1.777777780 + 2.666666667x + x2 = 2.5396825419 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 2.5396825419 Calculate the square root of the right side: 1.593638146 Break this problem into two subproblems by setting (x + 1.333333334) equal to 1.593638146 and -1.593638146.Subproblem 1
x + 1.333333334 = 1.593638146 Simplifying x + 1.333333334 = 1.593638146 Reorder the terms: 1.333333334 + x = 1.593638146 Solving 1.333333334 + x = 1.593638146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.593638146 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.593638146 + -1.333333334 x = 1.593638146 + -1.333333334 Combine like terms: 1.593638146 + -1.333333334 = 0.260304812 x = 0.260304812 Simplifying x = 0.260304812Subproblem 2
x + 1.333333334 = -1.593638146 Simplifying x + 1.333333334 = -1.593638146 Reorder the terms: 1.333333334 + x = -1.593638146 Solving 1.333333334 + x = -1.593638146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.593638146 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.593638146 + -1.333333334 x = -1.593638146 + -1.333333334 Combine like terms: -1.593638146 + -1.333333334 = -2.92697148 x = -2.92697148 Simplifying x = -2.92697148Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.260304812, -2.92697148}
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