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Simplifying 4x2 + 3x = 400 Reorder the terms: 3x + 4x2 = 400 Solving 3x + 4x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 3x + 4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -100 + 0.75x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 0.75x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 0.75x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 0.75x + x2 = 0 + 100 0.75x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 0.75x + x2 = 100 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 100 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 100 + 0.140625 Combine like terms: 100 + 0.140625 = 100.140625 0.140625 + 0.75x + x2 = 100.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 100.140625 Calculate the square root of the right side: 10.00702878 Break this problem into two subproblems by setting (x + 0.375) equal to 10.00702878 and -10.00702878.Subproblem 1
x + 0.375 = 10.00702878 Simplifying x + 0.375 = 10.00702878 Reorder the terms: 0.375 + x = 10.00702878 Solving 0.375 + x = 10.00702878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 10.00702878 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 10.00702878 + -0.375 x = 10.00702878 + -0.375 Combine like terms: 10.00702878 + -0.375 = 9.63202878 x = 9.63202878 Simplifying x = 9.63202878Subproblem 2
x + 0.375 = -10.00702878 Simplifying x + 0.375 = -10.00702878 Reorder the terms: 0.375 + x = -10.00702878 Solving 0.375 + x = -10.00702878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -10.00702878 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -10.00702878 + -0.375 x = -10.00702878 + -0.375 Combine like terms: -10.00702878 + -0.375 = -10.38202878 x = -10.38202878 Simplifying x = -10.38202878Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.63202878, -10.38202878}
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