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Simplifying 32x2 + -1x4 = 2 Solving 32x2 + -1x4 = 2 Solving for variable 'x'. Reorder the terms: -2 + 32x2 + -1x4 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 32x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -32x2 + x4 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -32x2 + -2 + x4 = 0 + -2 Reorder the terms: 2 + -2 + -32x2 + x4 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -32x2 + x4 = 0 + -2 -32x2 + x4 = 0 + -2 Combine like terms: 0 + -2 = -2 -32x2 + x4 = -2 The x term is -32x2. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x2 + 256 + x4 = -2 + 256 Reorder the terms: 256 + -32x2 + x4 = -2 + 256 Combine like terms: -2 + 256 = 254 256 + -32x2 + x4 = 254 Factor a perfect square on the left side: (x2 + -16)(x2 + -16) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x2 + -16) equal to 15.937377451 and -15.937377451.Subproblem 1
x2 + -16 = 15.937377451 Simplifying x2 + -16 = 15.937377451 Reorder the terms: -16 + x2 = 15.937377451 Solving -16 + x2 = 15.937377451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = 15.937377451 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 15.937377451 + 16 x2 = 15.937377451 + 16 Combine like terms: 15.937377451 + 16 = 31.937377451 x2 = 31.937377451 Simplifying x2 = 31.937377451 Take the square root of each side: x = {-5.651316435, 5.651316435}Subproblem 2
x2 + -16 = -15.937377451 Simplifying x2 + -16 = -15.937377451 Reorder the terms: -16 + x2 = -15.937377451 Solving -16 + x2 = -15.937377451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = -15.937377451 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -15.937377451 + 16 x2 = -15.937377451 + 16 Combine like terms: -15.937377451 + 16 = 0.062622549 x2 = 0.062622549 Simplifying x2 = 0.062622549 Take the square root of each side: x = {-0.250244978, 0.250244978}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.651316435, 5.651316435, -0.250244978, 0.250244978}
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