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Simplifying 4.905x2 + 9x + -20 = 0 Reorder the terms: -20 + 9x + 4.905x2 = 0 Solving -20 + 9x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -4.077471967 + 1.834862385x + x2 = 0 Move the constant term to the right: Add '4.077471967' to each side of the equation. -4.077471967 + 1.834862385x + 4.077471967 + x2 = 0 + 4.077471967 Reorder the terms: -4.077471967 + 4.077471967 + 1.834862385x + x2 = 0 + 4.077471967 Combine like terms: -4.077471967 + 4.077471967 = 0.000000000 0.000000000 + 1.834862385x + x2 = 0 + 4.077471967 1.834862385x + x2 = 0 + 4.077471967 Combine like terms: 0 + 4.077471967 = 4.077471967 1.834862385x + x2 = 4.077471967 The x term is 1.834862385x. Take half its coefficient (0.9174311925). Square it (0.8416799930) and add it to both sides. Add '0.8416799930' to each side of the equation. 1.834862385x + 0.8416799930 + x2 = 4.077471967 + 0.8416799930 Reorder the terms: 0.8416799930 + 1.834862385x + x2 = 4.077471967 + 0.8416799930 Combine like terms: 4.077471967 + 0.8416799930 = 4.91915196 0.8416799930 + 1.834862385x + x2 = 4.91915196 Factor a perfect square on the left side: (x + 0.9174311925)(x + 0.9174311925) = 4.91915196 Calculate the square root of the right side: 2.21791613 Break this problem into two subproblems by setting (x + 0.9174311925) equal to 2.21791613 and -2.21791613.Subproblem 1
x + 0.9174311925 = 2.21791613 Simplifying x + 0.9174311925 = 2.21791613 Reorder the terms: 0.9174311925 + x = 2.21791613 Solving 0.9174311925 + x = 2.21791613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9174311925' to each side of the equation. 0.9174311925 + -0.9174311925 + x = 2.21791613 + -0.9174311925 Combine like terms: 0.9174311925 + -0.9174311925 = 0.0000000000 0.0000000000 + x = 2.21791613 + -0.9174311925 x = 2.21791613 + -0.9174311925 Combine like terms: 2.21791613 + -0.9174311925 = 1.3004849375 x = 1.3004849375 Simplifying x = 1.3004849375Subproblem 2
x + 0.9174311925 = -2.21791613 Simplifying x + 0.9174311925 = -2.21791613 Reorder the terms: 0.9174311925 + x = -2.21791613 Solving 0.9174311925 + x = -2.21791613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9174311925' to each side of the equation. 0.9174311925 + -0.9174311925 + x = -2.21791613 + -0.9174311925 Combine like terms: 0.9174311925 + -0.9174311925 = 0.0000000000 0.0000000000 + x = -2.21791613 + -0.9174311925 x = -2.21791613 + -0.9174311925 Combine like terms: -2.21791613 + -0.9174311925 = -3.1353473225 x = -3.1353473225 Simplifying x = -3.1353473225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3004849375, -3.1353473225}
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