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Simplifying 4x2 + -21x + 7 = 0 Reorder the terms: 7 + -21x + 4x2 = 0 Solving 7 + -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'. 1.75 + -5.25x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -5.25x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -5.25x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -5.25x + x2 = 0 + -1.75 -5.25x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -5.25x + x2 = -1.75 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 = -1.75 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -1.75 + 6.890625 Combine like terms: -1.75 + 6.890625 = 5.140625 6.890625 + -5.25x + x2 = 5.140625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + -2.625) equal to 2.267294643 and -2.267294643.Subproblem 1
x + -2.625 = 2.267294643 Simplifying x + -2.625 = 2.267294643 Reorder the terms: -2.625 + x = 2.267294643 Solving -2.625 + x = 2.267294643 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 = 2.267294643 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.267294643 + 2.625 x = 2.267294643 + 2.625 Combine like terms: 2.267294643 + 2.625 = 4.892294643 x = 4.892294643 Simplifying x = 4.892294643Subproblem 2
x + -2.625 = -2.267294643 Simplifying x + -2.625 = -2.267294643 Reorder the terms: -2.625 + x = -2.267294643 Solving -2.625 + x = -2.267294643 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 = -2.267294643 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.267294643 + 2.625 x = -2.267294643 + 2.625 Combine like terms: -2.267294643 + 2.625 = 0.357705357 x = 0.357705357 Simplifying x = 0.357705357Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.892294643, 0.357705357}
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