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Simplifying 40x + -0.4x2 = 360 Solving 40x + -0.4x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 40x + -0.4x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 40x + -0.4x2 = 0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 900 + -100x + x2 = 0 Move the constant term to the right: Add '-900' to each side of the equation. 900 + -100x + -900 + x2 = 0 + -900 Reorder the terms: 900 + -900 + -100x + x2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + -100x + x2 = 0 + -900 -100x + x2 = 0 + -900 Combine like terms: 0 + -900 = -900 -100x + x2 = -900 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -900 + 2500 Reorder the terms: 2500 + -100x + x2 = -900 + 2500 Combine like terms: -900 + 2500 = 1600 2500 + -100x + x2 = 1600 Factor a perfect square on the left side: (x + -50)(x + -50) = 1600 Calculate the square root of the right side: 40 Break this problem into two subproblems by setting (x + -50) equal to 40 and -40.Subproblem 1
x + -50 = 40 Simplifying x + -50 = 40 Reorder the terms: -50 + x = 40 Solving -50 + x = 40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 40 + 50 Combine like terms: -50 + 50 = 0 0 + x = 40 + 50 x = 40 + 50 Combine like terms: 40 + 50 = 90 x = 90 Simplifying x = 90Subproblem 2
x + -50 = -40 Simplifying x + -50 = -40 Reorder the terms: -50 + x = -40 Solving -50 + x = -40 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -40 + 50 Combine like terms: -50 + 50 = 0 0 + x = -40 + 50 x = -40 + 50 Combine like terms: -40 + 50 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {90, 10}
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