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Simplifying 0 = -16x2 + -25x + 450 Reorder the terms: 0 = 450 + -25x + -16x2 Solving 0 = 450 + -25x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -450 = -450 -450 + 25x + 16x2 = 450 + -25x + -16x2 + -450 + 25x + 16x2 Reorder the terms: -450 + 25x + 16x2 = 450 + -450 + -25x + 25x + -16x2 + 16x2 Combine like terms: 450 + -450 = 0 -450 + 25x + 16x2 = 0 + -25x + 25x + -16x2 + 16x2 -450 + 25x + 16x2 = -25x + 25x + -16x2 + 16x2 Combine like terms: -25x + 25x = 0 -450 + 25x + 16x2 = 0 + -16x2 + 16x2 -450 + 25x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -450 + 25x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -28.125 + 1.5625x + x2 = 0 Move the constant term to the right: Add '28.125' to each side of the equation. -28.125 + 1.5625x + 28.125 + x2 = 0 + 28.125 Reorder the terms: -28.125 + 28.125 + 1.5625x + x2 = 0 + 28.125 Combine like terms: -28.125 + 28.125 = 0.000 0.000 + 1.5625x + x2 = 0 + 28.125 1.5625x + x2 = 0 + 28.125 Combine like terms: 0 + 28.125 = 28.125 1.5625x + x2 = 28.125 The x term is 1.5625x. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625x + 0.6103515625 + x2 = 28.125 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625x + x2 = 28.125 + 0.6103515625 Combine like terms: 28.125 + 0.6103515625 = 28.7353515625 0.6103515625 + 1.5625x + x2 = 28.7353515625 Factor a perfect square on the left side: (x + 0.78125)(x + 0.78125) = 28.7353515625 Calculate the square root of the right side: 5.3605365 Break this problem into two subproblems by setting (x + 0.78125) equal to 5.3605365 and -5.3605365.Subproblem 1
x + 0.78125 = 5.3605365 Simplifying x + 0.78125 = 5.3605365 Reorder the terms: 0.78125 + x = 5.3605365 Solving 0.78125 + x = 5.3605365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = 5.3605365 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = 5.3605365 + -0.78125 x = 5.3605365 + -0.78125 Combine like terms: 5.3605365 + -0.78125 = 4.5792865 x = 4.5792865 Simplifying x = 4.5792865Subproblem 2
x + 0.78125 = -5.3605365 Simplifying x + 0.78125 = -5.3605365 Reorder the terms: 0.78125 + x = -5.3605365 Solving 0.78125 + x = -5.3605365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = -5.3605365 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = -5.3605365 + -0.78125 x = -5.3605365 + -0.78125 Combine like terms: -5.3605365 + -0.78125 = -6.1417865 x = -6.1417865 Simplifying x = -6.1417865Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5792865, -6.1417865}
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