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Simplifying 0 = 4.9(x2) + 21x + -10 Reorder the terms: 0 = -10 + 21x + 4.9x2 Solving 0 = -10 + 21x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + -21x + -4.9x2 = -10 + 21x + 4.9x2 + 10 + -21x + -4.9x2 Reorder the terms: 10 + -21x + -4.9x2 = -10 + 10 + 21x + -21x + 4.9x2 + -4.9x2 Combine like terms: -10 + 10 = 0 10 + -21x + -4.9x2 = 0 + 21x + -21x + 4.9x2 + -4.9x2 10 + -21x + -4.9x2 = 21x + -21x + 4.9x2 + -4.9x2 Combine like terms: 21x + -21x = 0 10 + -21x + -4.9x2 = 0 + 4.9x2 + -4.9x2 10 + -21x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 10 + -21x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.040816327 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 4.285714286x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 4.285714286x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 4.285714286x + x2 = 0 + 2.040816327 4.285714286x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 4.285714286x + x2 = 2.040816327 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = 2.040816327 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = 2.040816327 + 4.591836735 Combine like terms: 2.040816327 + 4.591836735 = 6.632653062 4.591836735 + 4.285714286x + x2 = 6.632653062 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = 6.632653062 Calculate the square root of the right side: 2.575393768 Break this problem into two subproblems by setting (x + 2.142857143) equal to 2.575393768 and -2.575393768.Subproblem 1
x + 2.142857143 = 2.575393768 Simplifying x + 2.142857143 = 2.575393768 Reorder the terms: 2.142857143 + x = 2.575393768 Solving 2.142857143 + x = 2.575393768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = 2.575393768 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = 2.575393768 + -2.142857143 x = 2.575393768 + -2.142857143 Combine like terms: 2.575393768 + -2.142857143 = 0.432536625 x = 0.432536625 Simplifying x = 0.432536625Subproblem 2
x + 2.142857143 = -2.575393768 Simplifying x + 2.142857143 = -2.575393768 Reorder the terms: 2.142857143 + x = -2.575393768 Solving 2.142857143 + x = -2.575393768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = -2.575393768 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = -2.575393768 + -2.142857143 x = -2.575393768 + -2.142857143 Combine like terms: -2.575393768 + -2.142857143 = -4.718250911 x = -4.718250911 Simplifying x = -4.718250911Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.432536625, -4.718250911}
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