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Simplifying 0 = -16.8x2 + -0.9x + 5.22 Reorder the terms: 0 = 5.22 + -0.9x + -16.8x2 Solving 0 = 5.22 + -0.9x + -16.8x2 Solving for variable 'x'. Combine like terms: 0 + -5.22 = -5.22 -5.22 + 0.9x + 16.8x2 = 5.22 + -0.9x + -16.8x2 + -5.22 + 0.9x + 16.8x2 Reorder the terms: -5.22 + 0.9x + 16.8x2 = 5.22 + -5.22 + -0.9x + 0.9x + -16.8x2 + 16.8x2 Combine like terms: 5.22 + -5.22 = 0.00 -5.22 + 0.9x + 16.8x2 = 0.00 + -0.9x + 0.9x + -16.8x2 + 16.8x2 -5.22 + 0.9x + 16.8x2 = -0.9x + 0.9x + -16.8x2 + 16.8x2 Combine like terms: -0.9x + 0.9x = 0.0 -5.22 + 0.9x + 16.8x2 = 0.0 + -16.8x2 + 16.8x2 -5.22 + 0.9x + 16.8x2 = -16.8x2 + 16.8x2 Combine like terms: -16.8x2 + 16.8x2 = 0.0 -5.22 + 0.9x + 16.8x2 = 0.0 Begin completing the square. Divide all terms by 16.8 the coefficient of the squared term: Divide each side by '16.8'. -0.3107142857 + 0.05357142857x + x2 = 0 Move the constant term to the right: Add '0.3107142857' to each side of the equation. -0.3107142857 + 0.05357142857x + 0.3107142857 + x2 = 0 + 0.3107142857 Reorder the terms: -0.3107142857 + 0.3107142857 + 0.05357142857x + x2 = 0 + 0.3107142857 Combine like terms: -0.3107142857 + 0.3107142857 = 0.0000000000 0.0000000000 + 0.05357142857x + x2 = 0 + 0.3107142857 0.05357142857x + x2 = 0 + 0.3107142857 Combine like terms: 0 + 0.3107142857 = 0.3107142857 0.05357142857x + x2 = 0.3107142857 The x term is 0.05357142857x. Take half its coefficient (0.02678571429). Square it (0.0007174744900) and add it to both sides. Add '0.0007174744900' to each side of the equation. 0.05357142857x + 0.0007174744900 + x2 = 0.3107142857 + 0.0007174744900 Reorder the terms: 0.0007174744900 + 0.05357142857x + x2 = 0.3107142857 + 0.0007174744900 Combine like terms: 0.3107142857 + 0.0007174744900 = 0.31143176019 0.0007174744900 + 0.05357142857x + x2 = 0.31143176019 Factor a perfect square on the left side: (x + 0.02678571429)(x + 0.02678571429) = 0.31143176019 Calculate the square root of the right side: 0.558060714 Break this problem into two subproblems by setting (x + 0.02678571429) equal to 0.558060714 and -0.558060714.Subproblem 1
x + 0.02678571429 = 0.558060714 Simplifying x + 0.02678571429 = 0.558060714 Reorder the terms: 0.02678571429 + x = 0.558060714 Solving 0.02678571429 + x = 0.558060714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02678571429' to each side of the equation. 0.02678571429 + -0.02678571429 + x = 0.558060714 + -0.02678571429 Combine like terms: 0.02678571429 + -0.02678571429 = 0.00000000000 0.00000000000 + x = 0.558060714 + -0.02678571429 x = 0.558060714 + -0.02678571429 Combine like terms: 0.558060714 + -0.02678571429 = 0.53127499971 x = 0.53127499971 Simplifying x = 0.53127499971Subproblem 2
x + 0.02678571429 = -0.558060714 Simplifying x + 0.02678571429 = -0.558060714 Reorder the terms: 0.02678571429 + x = -0.558060714 Solving 0.02678571429 + x = -0.558060714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02678571429' to each side of the equation. 0.02678571429 + -0.02678571429 + x = -0.558060714 + -0.02678571429 Combine like terms: 0.02678571429 + -0.02678571429 = 0.00000000000 0.00000000000 + x = -0.558060714 + -0.02678571429 x = -0.558060714 + -0.02678571429 Combine like terms: -0.558060714 + -0.02678571429 = -0.58484642829 x = -0.58484642829 Simplifying x = -0.58484642829Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.53127499971, -0.58484642829}
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