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Simplifying x(x + 4) = 65 Reorder the terms: x(4 + x) = 65 (4 * x + x * x) = 65 (4x + x2) = 65 Solving 4x + x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 4x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 4x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 4x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 4x + x2 = 0 + 65 4x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 4x + x2 = 65 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 65 + 4 Reorder the terms: 4 + 4x + x2 = 65 + 4 Combine like terms: 65 + 4 = 69 4 + 4x + x2 = 69 Factor a perfect square on the left side: (x + 2)(x + 2) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 2) equal to 8.306623863 and -8.306623863.Subproblem 1
x + 2 = 8.306623863 Simplifying x + 2 = 8.306623863 Reorder the terms: 2 + x = 8.306623863 Solving 2 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.306623863 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.306623863 + -2 x = 8.306623863 + -2 Combine like terms: 8.306623863 + -2 = 6.306623863 x = 6.306623863 Simplifying x = 6.306623863Subproblem 2
x + 2 = -8.306623863 Simplifying x + 2 = -8.306623863 Reorder the terms: 2 + x = -8.306623863 Solving 2 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.306623863 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.306623863 + -2 x = -8.306623863 + -2 Combine like terms: -8.306623863 + -2 = -10.306623863 x = -10.306623863 Simplifying x = -10.306623863Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.306623863, -10.306623863}
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