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Simplifying 4x2 + -39x + 80 = 0 Reorder the terms: 80 + -39x + 4x2 = 0 Solving 80 + -39x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 20 + -9.75x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -9.75x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -9.75x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -9.75x + x2 = 0 + -20 -9.75x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -9.75x + x2 = -20 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -20 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -20 + 23.765625 Combine like terms: -20 + 23.765625 = 3.765625 23.765625 + -9.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + -4.875) equal to 1.940521837 and -1.940521837.Subproblem 1
x + -4.875 = 1.940521837 Simplifying x + -4.875 = 1.940521837 Reorder the terms: -4.875 + x = 1.940521837 Solving -4.875 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 1.940521837 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 1.940521837 + 4.875 x = 1.940521837 + 4.875 Combine like terms: 1.940521837 + 4.875 = 6.815521837 x = 6.815521837 Simplifying x = 6.815521837Subproblem 2
x + -4.875 = -1.940521837 Simplifying x + -4.875 = -1.940521837 Reorder the terms: -4.875 + x = -1.940521837 Solving -4.875 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -1.940521837 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -1.940521837 + 4.875 x = -1.940521837 + 4.875 Combine like terms: -1.940521837 + 4.875 = 2.934478163 x = 2.934478163 Simplifying x = 2.934478163Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.815521837, 2.934478163}
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