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Simplifying 6.75x2 + -21.8x + 16 = 0 Reorder the terms: 16 + -21.8x + 6.75x2 = 0 Solving 16 + -21.8x + 6.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.75 the coefficient of the squared term: Divide each side by '6.75'. 2.37037037 + -3.22962963x + x2 = 0 Move the constant term to the right: Add '-2.37037037' to each side of the equation. 2.37037037 + -3.22962963x + -2.37037037 + x2 = 0 + -2.37037037 Reorder the terms: 2.37037037 + -2.37037037 + -3.22962963x + x2 = 0 + -2.37037037 Combine like terms: 2.37037037 + -2.37037037 = 0.00000000 0.00000000 + -3.22962963x + x2 = 0 + -2.37037037 -3.22962963x + x2 = 0 + -2.37037037 Combine like terms: 0 + -2.37037037 = -2.37037037 -3.22962963x + x2 = -2.37037037 The x term is -3.22962963x. Take half its coefficient (-1.614814815). Square it (2.607626887) and add it to both sides. Add '2.607626887' to each side of the equation. -3.22962963x + 2.607626887 + x2 = -2.37037037 + 2.607626887 Reorder the terms: 2.607626887 + -3.22962963x + x2 = -2.37037037 + 2.607626887 Combine like terms: -2.37037037 + 2.607626887 = 0.237256517 2.607626887 + -3.22962963x + x2 = 0.237256517 Factor a perfect square on the left side: (x + -1.614814815)(x + -1.614814815) = 0.237256517 Calculate the square root of the right side: 0.487089845 Break this problem into two subproblems by setting (x + -1.614814815) equal to 0.487089845 and -0.487089845.Subproblem 1
x + -1.614814815 = 0.487089845 Simplifying x + -1.614814815 = 0.487089845 Reorder the terms: -1.614814815 + x = 0.487089845 Solving -1.614814815 + x = 0.487089845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.614814815' to each side of the equation. -1.614814815 + 1.614814815 + x = 0.487089845 + 1.614814815 Combine like terms: -1.614814815 + 1.614814815 = 0.000000000 0.000000000 + x = 0.487089845 + 1.614814815 x = 0.487089845 + 1.614814815 Combine like terms: 0.487089845 + 1.614814815 = 2.10190466 x = 2.10190466 Simplifying x = 2.10190466Subproblem 2
x + -1.614814815 = -0.487089845 Simplifying x + -1.614814815 = -0.487089845 Reorder the terms: -1.614814815 + x = -0.487089845 Solving -1.614814815 + x = -0.487089845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.614814815' to each side of the equation. -1.614814815 + 1.614814815 + x = -0.487089845 + 1.614814815 Combine like terms: -1.614814815 + 1.614814815 = 0.000000000 0.000000000 + x = -0.487089845 + 1.614814815 x = -0.487089845 + 1.614814815 Combine like terms: -0.487089845 + 1.614814815 = 1.12772497 x = 1.12772497 Simplifying x = 1.12772497Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.10190466, 1.12772497}
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