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Simplifying 4x2 + 24x + 21 = 0 Reorder the terms: 21 + 24x + 4x2 = 0 Solving 21 + 24x + 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'. 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 = 3.75 9 + 6x + x2 = 3.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + 3) equal to 1.936491673 and -1.936491673.Subproblem 1
x + 3 = 1.936491673 Simplifying x + 3 = 1.936491673 Reorder the terms: 3 + x = 1.936491673 Solving 3 + x = 1.936491673 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 = 1.936491673 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.936491673 + -3 x = 1.936491673 + -3 Combine like terms: 1.936491673 + -3 = -1.063508327 x = -1.063508327 Simplifying x = -1.063508327Subproblem 2
x + 3 = -1.936491673 Simplifying x + 3 = -1.936491673 Reorder the terms: 3 + x = -1.936491673 Solving 3 + x = -1.936491673 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 = -1.936491673 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.936491673 + -3 x = -1.936491673 + -3 Combine like terms: -1.936491673 + -3 = -4.936491673 x = -4.936491673 Simplifying x = -4.936491673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.063508327, -4.936491673}
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