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Simplifying 0 = -0.4x2 + 16x + 90 Reorder the terms: 0 = 90 + 16x + -0.4x2 Solving 0 = 90 + 16x + -0.4x2 Solving for variable 'x'. Combine like terms: 0 + -90 = -90 -90 + -16x + 0.4x2 = 90 + 16x + -0.4x2 + -90 + -16x + 0.4x2 Reorder the terms: -90 + -16x + 0.4x2 = 90 + -90 + 16x + -16x + -0.4x2 + 0.4x2 Combine like terms: 90 + -90 = 0 -90 + -16x + 0.4x2 = 0 + 16x + -16x + -0.4x2 + 0.4x2 -90 + -16x + 0.4x2 = 16x + -16x + -0.4x2 + 0.4x2 Combine like terms: 16x + -16x = 0 -90 + -16x + 0.4x2 = 0 + -0.4x2 + 0.4x2 -90 + -16x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 -90 + -16x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -225 + -40x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + -40x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + -40x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -40x + x2 = 0 + 225 -40x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 -40x + x2 = 225 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 225 + 400 Reorder the terms: 400 + -40x + x2 = 225 + 400 Combine like terms: 225 + 400 = 625 400 + -40x + x2 = 625 Factor a perfect square on the left side: (x + -20)(x + -20) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -20) equal to 25 and -25.Subproblem 1
x + -20 = 25 Simplifying x + -20 = 25 Reorder the terms: -20 + x = 25 Solving -20 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 25 + 20 Combine like terms: -20 + 20 = 0 0 + x = 25 + 20 x = 25 + 20 Combine like terms: 25 + 20 = 45 x = 45 Simplifying x = 45Subproblem 2
x + -20 = -25 Simplifying x + -20 = -25 Reorder the terms: -20 + x = -25 Solving -20 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -25 + 20 Combine like terms: -20 + 20 = 0 0 + x = -25 + 20 x = -25 + 20 Combine like terms: -25 + 20 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {45, -5}
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