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Simplifying 5(5 + 20) = x(16 + x) Combine like terms: 5 + 20 = 25 5(25) = x(16 + x) Multiply 5 * 25 125 = x(16 + x) 125 = (16 * x + x * x) 125 = (16x + x2) Solving 125 = 16x + x2 Solving for variable 'x'. Reorder the terms: 125 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 125 + -16x + -1x2 = 0 + x2 + -1x2 125 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 125 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -125 + 16x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 16x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 16x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 16x + x2 = 0 + 125 16x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 16x + x2 = 125 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 125 + 64 Reorder the terms: 64 + 16x + x2 = 125 + 64 Combine like terms: 125 + 64 = 189 64 + 16x + x2 = 189 Factor a perfect square on the left side: (x + 8)(x + 8) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + 8) equal to 13.747727085 and -13.747727085.Subproblem 1
x + 8 = 13.747727085 Simplifying x + 8 = 13.747727085 Reorder the terms: 8 + x = 13.747727085 Solving 8 + x = 13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 13.747727085 + -8 Combine like terms: 8 + -8 = 0 0 + x = 13.747727085 + -8 x = 13.747727085 + -8 Combine like terms: 13.747727085 + -8 = 5.747727085 x = 5.747727085 Simplifying x = 5.747727085Subproblem 2
x + 8 = -13.747727085 Simplifying x + 8 = -13.747727085 Reorder the terms: 8 + x = -13.747727085 Solving 8 + x = -13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -13.747727085 + -8 Combine like terms: 8 + -8 = 0 0 + x = -13.747727085 + -8 x = -13.747727085 + -8 Combine like terms: -13.747727085 + -8 = -21.747727085 x = -21.747727085 Simplifying x = -21.747727085Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.747727085, -21.747727085}
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