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Simplifying 12x2 + -84x + 1 = 0 Reorder the terms: 1 + -84x + 12x2 = 0 Solving 1 + -84x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + -7x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + -7x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + -7x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + -7x + x2 = 0 + -0.08333333333 -7x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 -7x + x2 = -0.08333333333 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.08333333333 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.08333333333 + 12.25 Combine like terms: -0.08333333333 + 12.25 = 12.16666666667 12.25 + -7x + x2 = 12.16666666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 12.16666666667 Calculate the square root of the right side: 3.488074923 Break this problem into two subproblems by setting (x + -3.5) equal to 3.488074923 and -3.488074923.Subproblem 1
x + -3.5 = 3.488074923 Simplifying x + -3.5 = 3.488074923 Reorder the terms: -3.5 + x = 3.488074923 Solving -3.5 + x = 3.488074923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.488074923 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.488074923 + 3.5 x = 3.488074923 + 3.5 Combine like terms: 3.488074923 + 3.5 = 6.988074923 x = 6.988074923 Simplifying x = 6.988074923Subproblem 2
x + -3.5 = -3.488074923 Simplifying x + -3.5 = -3.488074923 Reorder the terms: -3.5 + x = -3.488074923 Solving -3.5 + x = -3.488074923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.488074923 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.488074923 + 3.5 x = -3.488074923 + 3.5 Combine like terms: -3.488074923 + 3.5 = 0.011925077 x = 0.011925077 Simplifying x = 0.011925077Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.988074923, 0.011925077}
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