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Simplifying 21x2 + -21x + 4 = 0 Reorder the terms: 4 + -21x + 21x2 = 0 Solving 4 + -21x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.1904761905 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1904761905' to each side of the equation. 0.1904761905 + -1x + -0.1904761905 + x2 = 0 + -0.1904761905 Reorder the terms: 0.1904761905 + -0.1904761905 + -1x + x2 = 0 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.1904761905 -1x + x2 = 0 + -0.1904761905 Combine like terms: 0 + -0.1904761905 = -0.1904761905 -1x + x2 = -0.1904761905 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.1904761905 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1904761905 + 0.25 Combine like terms: -0.1904761905 + 0.25 = 0.0595238095 0.25 + -1x + x2 = 0.0595238095 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0595238095 Calculate the square root of the right side: 0.243975018 Break this problem into two subproblems by setting (x + -0.5) equal to 0.243975018 and -0.243975018.Subproblem 1
x + -0.5 = 0.243975018 Simplifying x + -0.5 = 0.243975018 Reorder the terms: -0.5 + x = 0.243975018 Solving -0.5 + x = 0.243975018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.243975018 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.243975018 + 0.5 x = 0.243975018 + 0.5 Combine like terms: 0.243975018 + 0.5 = 0.743975018 x = 0.743975018 Simplifying x = 0.743975018Subproblem 2
x + -0.5 = -0.243975018 Simplifying x + -0.5 = -0.243975018 Reorder the terms: -0.5 + x = -0.243975018 Solving -0.5 + x = -0.243975018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.243975018 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.243975018 + 0.5 x = -0.243975018 + 0.5 Combine like terms: -0.243975018 + 0.5 = 0.256024982 x = 0.256024982 Simplifying x = 0.256024982Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.743975018, 0.256024982}
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