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Simplifying -100 = 0.1x(30 + -1x) -100 = (30 * 0.1x + -1x * 0.1x) -100 = (3x + -0.1x2) Solving -100 = 3x + -0.1x2 Solving for variable 'x'. Reorder the terms: -100 + -3x + 0.1x2 = 3x + -3x + -0.1x2 + 0.1x2 Combine like terms: 3x + -3x = 0 -100 + -3x + 0.1x2 = 0 + -0.1x2 + 0.1x2 -100 + -3x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -100 + -3x + 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'. -1000 + -30x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -30x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -30x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -30x + x2 = 0 + 1000 -30x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -30x + x2 = 1000 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 1000 + 225 Reorder the terms: 225 + -30x + x2 = 1000 + 225 Combine like terms: 1000 + 225 = 1225 225 + -30x + x2 = 1225 Factor a perfect square on the left side: (x + -15)(x + -15) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (x + -15) equal to 35 and -35.Subproblem 1
x + -15 = 35 Simplifying x + -15 = 35 Reorder the terms: -15 + x = 35 Solving -15 + x = 35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 35 + 15 Combine like terms: -15 + 15 = 0 0 + x = 35 + 15 x = 35 + 15 Combine like terms: 35 + 15 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -15 = -35 Simplifying x + -15 = -35 Reorder the terms: -15 + x = -35 Solving -15 + x = -35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -35 + 15 Combine like terms: -15 + 15 = 0 0 + x = -35 + 15 x = -35 + 15 Combine like terms: -35 + 15 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -20}
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