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Simplifying 20 = 0.5(X + 4) * X Reorder the terms: 20 = 0.5(4 + X) * X Reorder the terms for easier multiplication: 20 = 0.5X(4 + X) 20 = (4 * 0.5X + X * 0.5X) 20 = (2X + 0.5X2) Solving 20 = 2X + 0.5X2 Solving for variable 'X'. Reorder the terms: 20 + -2X + -0.5X2 = 2X + -2X + 0.5X2 + -0.5X2 Combine like terms: 2X + -2X = 0 20 + -2X + -0.5X2 = 0 + 0.5X2 + -0.5X2 20 + -2X + -0.5X2 = 0.5X2 + -0.5X2 Combine like terms: 0.5X2 + -0.5X2 = 0.0 20 + -2X + -0.5X2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -40 + 4X + X2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 4X + 40 + X2 = 0 + 40 Reorder the terms: -40 + 40 + 4X + X2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 4X + X2 = 0 + 40 4X + X2 = 0 + 40 Combine like terms: 0 + 40 = 40 4X + X2 = 40 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 = 40 + 4 Reorder the terms: 4 + 4X + X2 = 40 + 4 Combine like terms: 40 + 4 = 44 4 + 4X + X2 = 44 Factor a perfect square on the left side: (X + 2)(X + 2) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (X + 2) equal to 6.633249581 and -6.633249581.Subproblem 1
X + 2 = 6.633249581 Simplifying X + 2 = 6.633249581 Reorder the terms: 2 + X = 6.633249581 Solving 2 + X = 6.633249581 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 = 6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + X = 6.633249581 + -2 X = 6.633249581 + -2 Combine like terms: 6.633249581 + -2 = 4.633249581 X = 4.633249581 Simplifying X = 4.633249581Subproblem 2
X + 2 = -6.633249581 Simplifying X + 2 = -6.633249581 Reorder the terms: 2 + X = -6.633249581 Solving 2 + X = -6.633249581 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 = -6.633249581 + -2 Combine like terms: 2 + -2 = 0 0 + X = -6.633249581 + -2 X = -6.633249581 + -2 Combine like terms: -6.633249581 + -2 = -8.633249581 X = -8.633249581 Simplifying X = -8.633249581Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.633249581, -8.633249581}
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