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Simplifying 16x2 + 32x = 73 Reorder the terms: 32x + 16x2 = 73 Solving 32x + 16x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 32x + 16x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 32x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.5625 + 2x + x2 = 0 Move the constant term to the right: Add '4.5625' to each side of the equation. -4.5625 + 2x + 4.5625 + x2 = 0 + 4.5625 Reorder the terms: -4.5625 + 4.5625 + 2x + x2 = 0 + 4.5625 Combine like terms: -4.5625 + 4.5625 = 0.0000 0.0000 + 2x + x2 = 0 + 4.5625 2x + x2 = 0 + 4.5625 Combine like terms: 0 + 4.5625 = 4.5625 2x + x2 = 4.5625 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 4.5625 + 1 Reorder the terms: 1 + 2x + x2 = 4.5625 + 1 Combine like terms: 4.5625 + 1 = 5.5625 1 + 2x + x2 = 5.5625 Factor a perfect square on the left side: (x + 1)(x + 1) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + 1) equal to 2.358495283 and -2.358495283.Subproblem 1
x + 1 = 2.358495283 Simplifying x + 1 = 2.358495283 Reorder the terms: 1 + x = 2.358495283 Solving 1 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.358495283 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.358495283 + -1 x = 2.358495283 + -1 Combine like terms: 2.358495283 + -1 = 1.358495283 x = 1.358495283 Simplifying x = 1.358495283Subproblem 2
x + 1 = -2.358495283 Simplifying x + 1 = -2.358495283 Reorder the terms: 1 + x = -2.358495283 Solving 1 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.358495283 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.358495283 + -1 x = -2.358495283 + -1 Combine like terms: -2.358495283 + -1 = -3.358495283 x = -3.358495283 Simplifying x = -3.358495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.358495283, -3.358495283}
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