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Simplifying 16x2 + 9x = 400 Reorder the terms: 9x + 16x2 = 400 Solving 9x + 16x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 9x + 16x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 9x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -25 + 0.5625x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 0.5625x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 0.5625x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 0.5625x + x2 = 0 + 25 0.5625x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 0.5625x + x2 = 25 The x term is 0.5625x. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625x + 0.0791015625 + x2 = 25 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 25 + 0.0791015625 Combine like terms: 25 + 0.0791015625 = 25.0791015625 0.0791015625 + 0.5625x + x2 = 25.0791015625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 25.0791015625 Calculate the square root of the right side: 5.007903909 Break this problem into two subproblems by setting (x + 0.28125) equal to 5.007903909 and -5.007903909.Subproblem 1
x + 0.28125 = 5.007903909 Simplifying x + 0.28125 = 5.007903909 Reorder the terms: 0.28125 + x = 5.007903909 Solving 0.28125 + x = 5.007903909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 5.007903909 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 5.007903909 + -0.28125 x = 5.007903909 + -0.28125 Combine like terms: 5.007903909 + -0.28125 = 4.726653909 x = 4.726653909 Simplifying x = 4.726653909Subproblem 2
x + 0.28125 = -5.007903909 Simplifying x + 0.28125 = -5.007903909 Reorder the terms: 0.28125 + x = -5.007903909 Solving 0.28125 + x = -5.007903909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -5.007903909 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -5.007903909 + -0.28125 x = -5.007903909 + -0.28125 Combine like terms: -5.007903909 + -0.28125 = -5.289153909 x = -5.289153909 Simplifying x = -5.289153909Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.726653909, -5.289153909}
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