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Simplifying 4x2 + 25x + -21 = x Reorder the terms: -21 + 25x + 4x2 = x Solving -21 + 25x + 4x2 = x Solving for variable 'x'. Reorder the terms: -21 + 25x + -1x + 4x2 = x + -1x Combine like terms: 25x + -1x = 24x -21 + 24x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -21 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 6x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 6x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 6x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 6x + x2 = 0 + 5.25 6x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 6x + x2 = 5.25 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 5.25 + 9 Reorder the terms: 9 + 6x + x2 = 5.25 + 9 Combine like terms: 5.25 + 9 = 14.25 9 + 6x + x2 = 14.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 3) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 3 = 3.774917218 Simplifying x + 3 = 3.774917218 Reorder the terms: 3 + x = 3.774917218 Solving 3 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.774917218 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.774917218 + -3 x = 3.774917218 + -3 Combine like terms: 3.774917218 + -3 = 0.774917218 x = 0.774917218 Simplifying x = 0.774917218Subproblem 2
x + 3 = -3.774917218 Simplifying x + 3 = -3.774917218 Reorder the terms: 3 + x = -3.774917218 Solving 3 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.774917218 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.774917218 + -3 x = -3.774917218 + -3 Combine like terms: -3.774917218 + -3 = -6.774917218 x = -6.774917218 Simplifying x = -6.774917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.774917218, -6.774917218}
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