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Simplifying 4.9x2 + -10x + -21 = 0 Reorder the terms: -21 + -10x + 4.9x2 = 0 Solving -21 + -10x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.285714286 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -2.040816327x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -2.040816327x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + 4.285714286 -2.040816327x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -2.040816327x + x2 = 4.285714286 The x term is -2.040816327x. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327x + 1.041232821 + x2 = 4.285714286 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 4.285714286 + 1.041232821 Combine like terms: 4.285714286 + 1.041232821 = 5.326947107 1.041232821 + -2.040816327x + x2 = 5.326947107 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 5.326947107 Calculate the square root of the right side: 2.308018004 Break this problem into two subproblems by setting (x + -1.020408164) equal to 2.308018004 and -2.308018004.Subproblem 1
x + -1.020408164 = 2.308018004 Simplifying x + -1.020408164 = 2.308018004 Reorder the terms: -1.020408164 + x = 2.308018004 Solving -1.020408164 + x = 2.308018004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = 2.308018004 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 2.308018004 + 1.020408164 x = 2.308018004 + 1.020408164 Combine like terms: 2.308018004 + 1.020408164 = 3.328426168 x = 3.328426168 Simplifying x = 3.328426168Subproblem 2
x + -1.020408164 = -2.308018004 Simplifying x + -1.020408164 = -2.308018004 Reorder the terms: -1.020408164 + x = -2.308018004 Solving -1.020408164 + x = -2.308018004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = -2.308018004 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -2.308018004 + 1.020408164 x = -2.308018004 + 1.020408164 Combine like terms: -2.308018004 + 1.020408164 = -1.28760984 x = -1.28760984 Simplifying x = -1.28760984Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.328426168, -1.28760984}
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