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Simplifying 16x2 + 35x = 125 Reorder the terms: 35x + 16x2 = 125 Solving 35x + 16x2 = 125 Solving for variable 'x'. Reorder the terms: -125 + 35x + 16x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 35x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.8125 + 2.1875x + x2 = 0 Move the constant term to the right: Add '7.8125' to each side of the equation. -7.8125 + 2.1875x + 7.8125 + x2 = 0 + 7.8125 Reorder the terms: -7.8125 + 7.8125 + 2.1875x + x2 = 0 + 7.8125 Combine like terms: -7.8125 + 7.8125 = 0.0000 0.0000 + 2.1875x + x2 = 0 + 7.8125 2.1875x + x2 = 0 + 7.8125 Combine like terms: 0 + 7.8125 = 7.8125 2.1875x + x2 = 7.8125 The x term is 2.1875x. Take half its coefficient (1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. 2.1875x + 1.196289063 + x2 = 7.8125 + 1.196289063 Reorder the terms: 1.196289063 + 2.1875x + x2 = 7.8125 + 1.196289063 Combine like terms: 7.8125 + 1.196289063 = 9.008789063 1.196289063 + 2.1875x + x2 = 9.008789063 Factor a perfect square on the left side: (x + 1.09375)(x + 1.09375) = 9.008789063 Calculate the square root of the right side: 3.001464486 Break this problem into two subproblems by setting (x + 1.09375) equal to 3.001464486 and -3.001464486.Subproblem 1
x + 1.09375 = 3.001464486 Simplifying x + 1.09375 = 3.001464486 Reorder the terms: 1.09375 + x = 3.001464486 Solving 1.09375 + x = 3.001464486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + x = 3.001464486 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + x = 3.001464486 + -1.09375 x = 3.001464486 + -1.09375 Combine like terms: 3.001464486 + -1.09375 = 1.907714486 x = 1.907714486 Simplifying x = 1.907714486Subproblem 2
x + 1.09375 = -3.001464486 Simplifying x + 1.09375 = -3.001464486 Reorder the terms: 1.09375 + x = -3.001464486 Solving 1.09375 + x = -3.001464486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + x = -3.001464486 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + x = -3.001464486 + -1.09375 x = -3.001464486 + -1.09375 Combine like terms: -3.001464486 + -1.09375 = -4.095214486 x = -4.095214486 Simplifying x = -4.095214486Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.907714486, -4.095214486}
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