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Simplifying 0 = (-4.9) * x2 + 28.13x + 20 Reorder the terms: 0 = 20 + 28.13x + -4.9x2 Solving 0 = 20 + 28.13x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -28.13x + 4.9x2 = 20 + 28.13x + -4.9x2 + -20 + -28.13x + 4.9x2 Reorder the terms: -20 + -28.13x + 4.9x2 = 20 + -20 + 28.13x + -28.13x + -4.9x2 + 4.9x2 Combine like terms: 20 + -20 = 0 -20 + -28.13x + 4.9x2 = 0 + 28.13x + -28.13x + -4.9x2 + 4.9x2 -20 + -28.13x + 4.9x2 = 28.13x + -28.13x + -4.9x2 + 4.9x2 Combine like terms: 28.13x + -28.13x = 0.00 -20 + -28.13x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -20 + -28.13x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -20 + -28.13x + 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'. -4.081632653 + -5.740816327x + x2 = 0 Move the constant term to the right: Add '4.081632653' to each side of the equation. -4.081632653 + -5.740816327x + 4.081632653 + x2 = 0 + 4.081632653 Reorder the terms: -4.081632653 + 4.081632653 + -5.740816327x + x2 = 0 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + -5.740816327x + x2 = 0 + 4.081632653 -5.740816327x + x2 = 0 + 4.081632653 Combine like terms: 0 + 4.081632653 = 4.081632653 -5.740816327x + x2 = 4.081632653 The x term is -5.740816327x. Take half its coefficient (-2.870408164). Square it (8.239243028) and add it to both sides. Add '8.239243028' to each side of the equation. -5.740816327x + 8.239243028 + x2 = 4.081632653 + 8.239243028 Reorder the terms: 8.239243028 + -5.740816327x + x2 = 4.081632653 + 8.239243028 Combine like terms: 4.081632653 + 8.239243028 = 12.320875681 8.239243028 + -5.740816327x + x2 = 12.320875681 Factor a perfect square on the left side: (x + -2.870408164)(x + -2.870408164) = 12.320875681 Calculate the square root of the right side: 3.510110494 Break this problem into two subproblems by setting (x + -2.870408164) equal to 3.510110494 and -3.510110494.Subproblem 1
x + -2.870408164 = 3.510110494 Simplifying x + -2.870408164 = 3.510110494 Reorder the terms: -2.870408164 + x = 3.510110494 Solving -2.870408164 + x = 3.510110494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.870408164' to each side of the equation. -2.870408164 + 2.870408164 + x = 3.510110494 + 2.870408164 Combine like terms: -2.870408164 + 2.870408164 = 0.000000000 0.000000000 + x = 3.510110494 + 2.870408164 x = 3.510110494 + 2.870408164 Combine like terms: 3.510110494 + 2.870408164 = 6.380518658 x = 6.380518658 Simplifying x = 6.380518658Subproblem 2
x + -2.870408164 = -3.510110494 Simplifying x + -2.870408164 = -3.510110494 Reorder the terms: -2.870408164 + x = -3.510110494 Solving -2.870408164 + x = -3.510110494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.870408164' to each side of the equation. -2.870408164 + 2.870408164 + x = -3.510110494 + 2.870408164 Combine like terms: -2.870408164 + 2.870408164 = 0.000000000 0.000000000 + x = -3.510110494 + 2.870408164 x = -3.510110494 + 2.870408164 Combine like terms: -3.510110494 + 2.870408164 = -0.63970233 x = -0.63970233 Simplifying x = -0.63970233Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.380518658, -0.63970233}
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