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Simplifying 400 = 0.1x2 + 3x Reorder the terms: 400 = 3x + 0.1x2 Solving 400 = 3x + 0.1x2 Solving for variable 'x'. Reorder the terms: 400 + -3x + -0.1x2 = 3x + -3x + 0.1x2 + -0.1x2 Combine like terms: 3x + -3x = 0 400 + -3x + -0.1x2 = 0 + 0.1x2 + -0.1x2 400 + -3x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 400 + -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'. -4000 + 30x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 30x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 30x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 30x + x2 = 0 + 4000 30x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 30x + x2 = 4000 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 = 4000 + 225 Reorder the terms: 225 + 30x + x2 = 4000 + 225 Combine like terms: 4000 + 225 = 4225 225 + 30x + x2 = 4225 Factor a perfect square on the left side: (x + 15)(x + 15) = 4225 Calculate the square root of the right side: 65 Break this problem into two subproblems by setting (x + 15) equal to 65 and -65.Subproblem 1
x + 15 = 65 Simplifying x + 15 = 65 Reorder the terms: 15 + x = 65 Solving 15 + x = 65 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 = 65 + -15 Combine like terms: 15 + -15 = 0 0 + x = 65 + -15 x = 65 + -15 Combine like terms: 65 + -15 = 50 x = 50 Simplifying x = 50Subproblem 2
x + 15 = -65 Simplifying x + 15 = -65 Reorder the terms: 15 + x = -65 Solving 15 + x = -65 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 = -65 + -15 Combine like terms: 15 + -15 = 0 0 + x = -65 + -15 x = -65 + -15 Combine like terms: -65 + -15 = -80 x = -80 Simplifying x = -80Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -80}
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