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Simplifying 8x2 + 16x2 + 256x + 4 = 0 Reorder the terms: 4 + 256x + 8x2 + 16x2 = 0 Combine like terms: 8x2 + 16x2 = 24x2 4 + 256x + 24x2 = 0 Solving 4 + 256x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 64x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 64x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + 64x + 6x2 = 0 Solving 1 + 64x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 10.66666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 10.66666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 10.66666667x + x2 = 0 + -0.1666666667 10.66666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 10.66666667x + x2 = -0.1666666667 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = -0.1666666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = -0.1666666667 + 28.44444446 Combine like terms: -0.1666666667 + 28.44444446 = 28.2777777933 28.44444446 + 10.66666667x + x2 = 28.2777777933 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 28.2777777933 Calculate the square root of the right side: 5.317685379 Break this problem into two subproblems by setting (x + 5.333333335) equal to 5.317685379 and -5.317685379.Subproblem 1
x + 5.333333335 = 5.317685379 Simplifying x + 5.333333335 = 5.317685379 Reorder the terms: 5.333333335 + x = 5.317685379 Solving 5.333333335 + x = 5.317685379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 5.317685379 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 5.317685379 + -5.333333335 x = 5.317685379 + -5.333333335 Combine like terms: 5.317685379 + -5.333333335 = -0.015647956 x = -0.015647956 Simplifying x = -0.015647956Subproblem 2
x + 5.333333335 = -5.317685379 Simplifying x + 5.333333335 = -5.317685379 Reorder the terms: 5.333333335 + x = -5.317685379 Solving 5.333333335 + x = -5.317685379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -5.317685379 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -5.317685379 + -5.333333335 x = -5.317685379 + -5.333333335 Combine like terms: -5.317685379 + -5.333333335 = -10.651018714 x = -10.651018714 Simplifying x = -10.651018714Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.015647956, -10.651018714}Solution
x = {-0.015647956, -10.651018714}
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