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Simplifying -0.01x2 + 0.4x + 5 = 0 Reorder the terms: 5 + 0.4x + -0.01x2 = 0 Solving 5 + 0.4x + -0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -500 + -40x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -40x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -40x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -40x + x2 = 0 + 500 -40x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -40x + x2 = 500 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 = 500 + 400 Reorder the terms: 400 + -40x + x2 = 500 + 400 Combine like terms: 500 + 400 = 900 400 + -40x + x2 = 900 Factor a perfect square on the left side: (x + -20)(x + -20) = 900 Calculate the square root of the right side: 30 Break this problem into two subproblems by setting (x + -20) equal to 30 and -30.Subproblem 1
x + -20 = 30 Simplifying x + -20 = 30 Reorder the terms: -20 + x = 30 Solving -20 + x = 30 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 = 30 + 20 Combine like terms: -20 + 20 = 0 0 + x = 30 + 20 x = 30 + 20 Combine like terms: 30 + 20 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -20 = -30 Simplifying x + -20 = -30 Reorder the terms: -20 + x = -30 Solving -20 + x = -30 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 = -30 + 20 Combine like terms: -20 + 20 = 0 0 + x = -30 + 20 x = -30 + 20 Combine like terms: -30 + 20 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -10}
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