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Simplifying x2 + 16x2 + 16x + 16x + 16 = 36 Reorder the terms: 16 + 16x + 16x + x2 + 16x2 = 36 Combine like terms: 16x + 16x = 32x 16 + 32x + x2 + 16x2 = 36 Combine like terms: x2 + 16x2 = 17x2 16 + 32x + 17x2 = 36 Solving 16 + 32x + 17x2 = 36 Solving for variable 'x'. Reorder the terms: 16 + -36 + 32x + 17x2 = 36 + -36 Combine like terms: 16 + -36 = -20 -20 + 32x + 17x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -20 + 32x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.176470588 + 1.882352941x + x2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + 1.882352941x + 1.176470588 + x2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + 1.882352941x + x2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + 1.882352941x + x2 = 0 + 1.176470588 1.882352941x + x2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 1.882352941x + x2 = 1.176470588 The x term is 1.882352941x. Take half its coefficient (0.9411764705). Square it (0.8858131486) and add it to both sides. Add '0.8858131486' to each side of the equation. 1.882352941x + 0.8858131486 + x2 = 1.176470588 + 0.8858131486 Reorder the terms: 0.8858131486 + 1.882352941x + x2 = 1.176470588 + 0.8858131486 Combine like terms: 1.176470588 + 0.8858131486 = 2.0622837366 0.8858131486 + 1.882352941x + x2 = 2.0622837366 Factor a perfect square on the left side: (x + 0.9411764705)(x + 0.9411764705) = 2.0622837366 Calculate the square root of the right side: 1.436065366 Break this problem into two subproblems by setting (x + 0.9411764705) equal to 1.436065366 and -1.436065366.Subproblem 1
x + 0.9411764705 = 1.436065366 Simplifying x + 0.9411764705 = 1.436065366 Reorder the terms: 0.9411764705 + x = 1.436065366 Solving 0.9411764705 + x = 1.436065366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = 1.436065366 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = 1.436065366 + -0.9411764705 x = 1.436065366 + -0.9411764705 Combine like terms: 1.436065366 + -0.9411764705 = 0.4948888955 x = 0.4948888955 Simplifying x = 0.4948888955Subproblem 2
x + 0.9411764705 = -1.436065366 Simplifying x + 0.9411764705 = -1.436065366 Reorder the terms: 0.9411764705 + x = -1.436065366 Solving 0.9411764705 + x = -1.436065366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9411764705' to each side of the equation. 0.9411764705 + -0.9411764705 + x = -1.436065366 + -0.9411764705 Combine like terms: 0.9411764705 + -0.9411764705 = 0.0000000000 0.0000000000 + x = -1.436065366 + -0.9411764705 x = -1.436065366 + -0.9411764705 Combine like terms: -1.436065366 + -0.9411764705 = -2.3772418365 x = -2.3772418365 Simplifying x = -2.3772418365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4948888955, -2.3772418365}
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