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Simplifying (8x * 8x) + 6x + -6 = 0 Reorder the terms for easier multiplication: (8 * 8x * x) + 6x + -6 = 0 Multiply 8 * 8 (64x * x) + 6x + -6 = 0 Multiply x * x (64x2) + 6x + -6 = 0 Reorder the terms: -6 + 6x + (64x2) = 0 Solving -6 + 6x + (64x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 3x + (32x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 3x + (32x2))' equal to zero and attempt to solve: Simplifying -3 + 3x + (32x2) = 0 Solving -3 + 3x + (32x2) = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.09375 + 0.09375x + x2 = 0 Move the constant term to the right: Add '0.09375' to each side of the equation. -0.09375 + 0.09375x + 0.09375 + x2 = 0 + 0.09375 Reorder the terms: -0.09375 + 0.09375 + 0.09375x + x2 = 0 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + 0.09375x + x2 = 0 + 0.09375 0.09375x + x2 = 0 + 0.09375 Combine like terms: 0 + 0.09375 = 0.09375 0.09375x + x2 = 0.09375 The x term is 0.09375x. Take half its coefficient (0.046875). Square it (0.002197265625) and add it to both sides. Add '0.002197265625' to each side of the equation. 0.09375x + 0.002197265625 + x2 = 0.09375 + 0.002197265625 Reorder the terms: 0.002197265625 + 0.09375x + x2 = 0.09375 + 0.002197265625 Combine like terms: 0.09375 + 0.002197265625 = 0.095947265625 0.002197265625 + 0.09375x + x2 = 0.095947265625 Factor a perfect square on the left side: ((x) + 0.046875)((x) + 0.046875) = 0.095947265625 Calculate the square root of the right side: 0.309753556 Break this problem into two subproblems by setting ((x) + 0.046875) equal to 0.309753556 and -0.309753556.Subproblem 1
(x) + 0.046875 = 0.309753556 Simplifying (x) + 0.046875 = 0.309753556 x + 0.046875 = 0.309753556 Reorder the terms: 0.046875 + x = 0.309753556 Solving 0.046875 + x = 0.309753556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = 0.309753556 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = 0.309753556 + -0.046875 x = 0.309753556 + -0.046875 Combine like terms: 0.309753556 + -0.046875 = 0.262878556 x = 0.262878556 Simplifying x = 0.262878556Subproblem 2
(x) + 0.046875 = -0.309753556 Simplifying (x) + 0.046875 = -0.309753556 x + 0.046875 = -0.309753556 Reorder the terms: 0.046875 + x = -0.309753556 Solving 0.046875 + x = -0.309753556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = -0.309753556 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = -0.309753556 + -0.046875 x = -0.309753556 + -0.046875 Combine like terms: -0.309753556 + -0.046875 = -0.356628556 x = -0.356628556 Simplifying x = -0.356628556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.262878556, -0.356628556}Solution
x = {0.262878556, -0.356628556}
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