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Simplifying 4x2 + -21x + 9 = 0 Reorder the terms: 9 + -21x + 4x2 = 0 Solving 9 + -21x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -5.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -5.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -5.25x + x2 = 0 + -2.25 -5.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -5.25x + x2 = -2.25 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -2.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -2.25 + 6.890625 Combine like terms: -2.25 + 6.890625 = 4.640625 6.890625 + -5.25x + x2 = 4.640625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + -2.625) equal to 2.154210992 and -2.154210992.Subproblem 1
x + -2.625 = 2.154210992 Simplifying x + -2.625 = 2.154210992 Reorder the terms: -2.625 + x = 2.154210992 Solving -2.625 + x = 2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.154210992 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.154210992 + 2.625 x = 2.154210992 + 2.625 Combine like terms: 2.154210992 + 2.625 = 4.779210992 x = 4.779210992 Simplifying x = 4.779210992Subproblem 2
x + -2.625 = -2.154210992 Simplifying x + -2.625 = -2.154210992 Reorder the terms: -2.625 + x = -2.154210992 Solving -2.625 + x = -2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.154210992 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.154210992 + 2.625 x = -2.154210992 + 2.625 Combine like terms: -2.154210992 + 2.625 = 0.470789008 x = 0.470789008 Simplifying x = 0.470789008Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.779210992, 0.470789008}
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