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Simplifying 4.9x2 + -10x + -77 = 0 Reorder the terms: -77 + -10x + 4.9x2 = 0 Solving -77 + -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'. -15.71428571 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '15.71428571' to each side of the equation. -15.71428571 + -2.040816327x + 15.71428571 + x2 = 0 + 15.71428571 Reorder the terms: -15.71428571 + 15.71428571 + -2.040816327x + x2 = 0 + 15.71428571 Combine like terms: -15.71428571 + 15.71428571 = 0.00000000 0.00000000 + -2.040816327x + x2 = 0 + 15.71428571 -2.040816327x + x2 = 0 + 15.71428571 Combine like terms: 0 + 15.71428571 = 15.71428571 -2.040816327x + x2 = 15.71428571 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 = 15.71428571 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 15.71428571 + 1.041232821 Combine like terms: 15.71428571 + 1.041232821 = 16.755518531 1.041232821 + -2.040816327x + x2 = 16.755518531 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 16.755518531 Calculate the square root of the right side: 4.093350526 Break this problem into two subproblems by setting (x + -1.020408164) equal to 4.093350526 and -4.093350526.Subproblem 1
x + -1.020408164 = 4.093350526 Simplifying x + -1.020408164 = 4.093350526 Reorder the terms: -1.020408164 + x = 4.093350526 Solving -1.020408164 + x = 4.093350526 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 = 4.093350526 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 4.093350526 + 1.020408164 x = 4.093350526 + 1.020408164 Combine like terms: 4.093350526 + 1.020408164 = 5.11375869 x = 5.11375869 Simplifying x = 5.11375869Subproblem 2
x + -1.020408164 = -4.093350526 Simplifying x + -1.020408164 = -4.093350526 Reorder the terms: -1.020408164 + x = -4.093350526 Solving -1.020408164 + x = -4.093350526 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 = -4.093350526 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -4.093350526 + 1.020408164 x = -4.093350526 + 1.020408164 Combine like terms: -4.093350526 + 1.020408164 = -3.072942362 x = -3.072942362 Simplifying x = -3.072942362Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.11375869, -3.072942362}
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