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Simplifying 400 = -2.5x2 + 100x + -300 Reorder the terms: 400 = -300 + 100x + -2.5x2 Solving 400 = -300 + 100x + -2.5x2 Solving for variable 'x'. Combine like terms: 400 + 300 = 700 700 + -100x + 2.5x2 = -300 + 100x + -2.5x2 + 300 + -100x + 2.5x2 Reorder the terms: 700 + -100x + 2.5x2 = -300 + 300 + 100x + -100x + -2.5x2 + 2.5x2 Combine like terms: -300 + 300 = 0 700 + -100x + 2.5x2 = 0 + 100x + -100x + -2.5x2 + 2.5x2 700 + -100x + 2.5x2 = 100x + -100x + -2.5x2 + 2.5x2 Combine like terms: 100x + -100x = 0 700 + -100x + 2.5x2 = 0 + -2.5x2 + 2.5x2 700 + -100x + 2.5x2 = -2.5x2 + 2.5x2 Combine like terms: -2.5x2 + 2.5x2 = 0.0 700 + -100x + 2.5x2 = 0.0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 280 + -40x + x2 = 0 Move the constant term to the right: Add '-280' to each side of the equation. 280 + -40x + -280 + x2 = 0 + -280 Reorder the terms: 280 + -280 + -40x + x2 = 0 + -280 Combine like terms: 280 + -280 = 0 0 + -40x + x2 = 0 + -280 -40x + x2 = 0 + -280 Combine like terms: 0 + -280 = -280 -40x + x2 = -280 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 = -280 + 400 Reorder the terms: 400 + -40x + x2 = -280 + 400 Combine like terms: -280 + 400 = 120 400 + -40x + x2 = 120 Factor a perfect square on the left side: (x + -20)(x + -20) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + -20) equal to 10.95445115 and -10.95445115.Subproblem 1
x + -20 = 10.95445115 Simplifying x + -20 = 10.95445115 Reorder the terms: -20 + x = 10.95445115 Solving -20 + x = 10.95445115 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 = 10.95445115 + 20 Combine like terms: -20 + 20 = 0 0 + x = 10.95445115 + 20 x = 10.95445115 + 20 Combine like terms: 10.95445115 + 20 = 30.95445115 x = 30.95445115 Simplifying x = 30.95445115Subproblem 2
x + -20 = -10.95445115 Simplifying x + -20 = -10.95445115 Reorder the terms: -20 + x = -10.95445115 Solving -20 + x = -10.95445115 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 = -10.95445115 + 20 Combine like terms: -20 + 20 = 0 0 + x = -10.95445115 + 20 x = -10.95445115 + 20 Combine like terms: -10.95445115 + 20 = 9.04554885 x = 9.04554885 Simplifying x = 9.04554885Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.95445115, 9.04554885}
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