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Simplifying 4x(x + 4) = 9 + -16x Reorder the terms: 4x(4 + x) = 9 + -16x (4 * 4x + x * 4x) = 9 + -16x (16x + 4x2) = 9 + -16x Solving 16x + 4x2 = 9 + -16x Solving for variable 'x'. Reorder the terms: -9 + 16x + 16x + 4x2 = 9 + -16x + -9 + 16x Combine like terms: 16x + 16x = 32x -9 + 32x + 4x2 = 9 + -16x + -9 + 16x Reorder the terms: -9 + 32x + 4x2 = 9 + -9 + -16x + 16x Combine like terms: 9 + -9 = 0 -9 + 32x + 4x2 = 0 + -16x + 16x -9 + 32x + 4x2 = -16x + 16x Combine like terms: -16x + 16x = 0 -9 + 32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 8x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 8x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 8x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 8x + x2 = 0 + 2.25 8x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 8x + x2 = 2.25 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 2.25 + 16 Reorder the terms: 16 + 8x + x2 = 2.25 + 16 Combine like terms: 2.25 + 16 = 18.25 16 + 8x + x2 = 18.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 4) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 4 = 4.272001873 Simplifying x + 4 = 4.272001873 Reorder the terms: 4 + x = 4.272001873 Solving 4 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.272001873 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.272001873 + -4 x = 4.272001873 + -4 Combine like terms: 4.272001873 + -4 = 0.272001873 x = 0.272001873 Simplifying x = 0.272001873Subproblem 2
x + 4 = -4.272001873 Simplifying x + 4 = -4.272001873 Reorder the terms: 4 + x = -4.272001873 Solving 4 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.272001873 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.272001873 + -4 x = -4.272001873 + -4 Combine like terms: -4.272001873 + -4 = -8.272001873 x = -8.272001873 Simplifying x = -8.272001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.272001873, -8.272001873}
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