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Simplifying 4.9x2 + 10x + -20 = 0 Reorder the terms: -20 + 10x + 4.9x2 = 0 Solving -20 + 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'. -4.081632653 + 2.040816327x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + 2.040816327x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + 2.040816327x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + 2.040816327x + x2 = 0 + 4.081632653 2.040816327x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 2.040816327x + x2 = 4.081632653 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 = 4.081632653 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327x + x2 = 4.081632653 + 1.041232821 Combine like terms: 4.081632653 + 1.041232821 = 5.122865474 1.041232821 + 2.040816327x + x2 = 5.122865474 Factor a perfect square on the left side: (x + 1.020408164)(x + 1.020408164) = 5.122865474 Calculate the square root of the right side: 2.263374798 Break this problem into two subproblems by setting (x + 1.020408164) equal to 2.263374798 and -2.263374798.Subproblem 1
x + 1.020408164 = 2.263374798 Simplifying x + 1.020408164 = 2.263374798 Reorder the terms: 1.020408164 + x = 2.263374798 Solving 1.020408164 + x = 2.263374798 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 = 2.263374798 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 2.263374798 + -1.020408164 x = 2.263374798 + -1.020408164 Combine like terms: 2.263374798 + -1.020408164 = 1.242966634 x = 1.242966634 Simplifying x = 1.242966634Subproblem 2
x + 1.020408164 = -2.263374798 Simplifying x + 1.020408164 = -2.263374798 Reorder the terms: 1.020408164 + x = -2.263374798 Solving 1.020408164 + x = -2.263374798 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 = -2.263374798 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -2.263374798 + -1.020408164 x = -2.263374798 + -1.020408164 Combine like terms: -2.263374798 + -1.020408164 = -3.283782962 x = -3.283782962 Simplifying x = -3.283782962Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242966634, -3.283782962}
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