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Simplifying 16 = 0.6X + 0.1X2 Solving 16 = 0.6X + 0.1X2 Solving for variable 'X'. Reorder the terms: 16 + -0.6X + -0.1X2 = 0.6X + -0.6X + 0.1X2 + -0.1X2 Combine like terms: 0.6X + -0.6X = 0.0 16 + -0.6X + -0.1X2 = 0.0 + 0.1X2 + -0.1X2 16 + -0.6X + -0.1X2 = 0.1X2 + -0.1X2 Combine like terms: 0.1X2 + -0.1X2 = 0.0 16 + -0.6X + -0.1X2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -160 + 6X + X2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 6X + 160 + X2 = 0 + 160 Reorder the terms: -160 + 160 + 6X + X2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 6X + X2 = 0 + 160 6X + X2 = 0 + 160 Combine like terms: 0 + 160 = 160 6X + X2 = 160 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 = 160 + 9 Reorder the terms: 9 + 6X + X2 = 160 + 9 Combine like terms: 160 + 9 = 169 9 + 6X + X2 = 169 Factor a perfect square on the left side: (X + 3)(X + 3) = 169 Calculate the square root of the right side: 13 Break this problem into two subproblems by setting (X + 3) equal to 13 and -13.Subproblem 1
X + 3 = 13 Simplifying X + 3 = 13 Reorder the terms: 3 + X = 13 Solving 3 + X = 13 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 = 13 + -3 Combine like terms: 3 + -3 = 0 0 + X = 13 + -3 X = 13 + -3 Combine like terms: 13 + -3 = 10 X = 10 Simplifying X = 10Subproblem 2
X + 3 = -13 Simplifying X + 3 = -13 Reorder the terms: 3 + X = -13 Solving 3 + X = -13 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 = -13 + -3 Combine like terms: 3 + -3 = 0 0 + X = -13 + -3 X = -13 + -3 Combine like terms: -13 + -3 = -16 X = -16 Simplifying X = -16Solution
The solution to the problem is based on the solutions from the subproblems. X = {10, -16}
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