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Simplifying -4.9x2 + 100x + 20 = 0 Reorder the terms: 20 + 100x + -4.9x2 = 0 Solving 20 + 100x + -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'. -4.081632653 + -20.40816327x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -20.40816327x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -20.40816327x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -20.40816327x + x2 = 0 + 4.081632653 -20.40816327x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -20.40816327x + x2 = 4.081632653 The x term is -20.40816327x. Take half its coefficient (-10.20408164). Square it (104.1232821) and add it to both sides. Add '104.1232821' to each side of the equation. -20.40816327x + 104.1232821 + x2 = 4.081632653 + 104.1232821 Reorder the terms: 104.1232821 + -20.40816327x + x2 = 4.081632653 + 104.1232821 Combine like terms: 4.081632653 + 104.1232821 = 108.204914753 104.1232821 + -20.40816327x + x2 = 108.204914753 Factor a perfect square on the left side: (x + -10.20408164)(x + -10.20408164) = 108.204914753 Calculate the square root of the right side: 10.402159139 Break this problem into two subproblems by setting (x + -10.20408164) equal to 10.402159139 and -10.402159139.Subproblem 1
x + -10.20408164 = 10.402159139 Simplifying x + -10.20408164 = 10.402159139 Reorder the terms: -10.20408164 + x = 10.402159139 Solving -10.20408164 + x = 10.402159139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = 10.402159139 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = 10.402159139 + 10.20408164 x = 10.402159139 + 10.20408164 Combine like terms: 10.402159139 + 10.20408164 = 20.606240779 x = 20.606240779 Simplifying x = 20.606240779Subproblem 2
x + -10.20408164 = -10.402159139 Simplifying x + -10.20408164 = -10.402159139 Reorder the terms: -10.20408164 + x = -10.402159139 Solving -10.20408164 + x = -10.402159139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = -10.402159139 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = -10.402159139 + 10.20408164 x = -10.402159139 + 10.20408164 Combine like terms: -10.402159139 + 10.20408164 = -0.198077499 x = -0.198077499 Simplifying x = -0.198077499Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.606240779, -0.198077499}
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