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Simplifying 8x(8x) + 6x = 9 Remove parenthesis around (8x) 8x * 8x + 6x = 9 Reorder the terms for easier multiplication: 8 * 8x * x + 6x = 9 Multiply 8 * 8 64x * x + 6x = 9 Multiply x * x 64x2 + 6x = 9 Reorder the terms: 6x + 64x2 = 9 Solving 6x + 64x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 6x + 64x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.140625 + 0.09375x + x2 = 0 Move the constant term to the right: Add '0.140625' to each side of the equation. -0.140625 + 0.09375x + 0.140625 + x2 = 0 + 0.140625 Reorder the terms: -0.140625 + 0.140625 + 0.09375x + x2 = 0 + 0.140625 Combine like terms: -0.140625 + 0.140625 = 0.000000 0.000000 + 0.09375x + x2 = 0 + 0.140625 0.09375x + x2 = 0 + 0.140625 Combine like terms: 0 + 0.140625 = 0.140625 0.09375x + x2 = 0.140625 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 = 0.140625 + 0.002197265625 Reorder the terms: 0.002197265625 + 0.09375x + x2 = 0.140625 + 0.002197265625 Combine like terms: 0.140625 + 0.002197265625 = 0.142822265625 0.002197265625 + 0.09375x + x2 = 0.142822265625 Factor a perfect square on the left side: (x + 0.046875)(x + 0.046875) = 0.142822265625 Calculate the square root of the right side: 0.377918332 Break this problem into two subproblems by setting (x + 0.046875) equal to 0.377918332 and -0.377918332.Subproblem 1
x + 0.046875 = 0.377918332 Simplifying x + 0.046875 = 0.377918332 Reorder the terms: 0.046875 + x = 0.377918332 Solving 0.046875 + x = 0.377918332 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 = 0.377918332 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = 0.377918332 + -0.046875 x = 0.377918332 + -0.046875 Combine like terms: 0.377918332 + -0.046875 = 0.331043332 x = 0.331043332 Simplifying x = 0.331043332Subproblem 2
x + 0.046875 = -0.377918332 Simplifying x + 0.046875 = -0.377918332 Reorder the terms: 0.046875 + x = -0.377918332 Solving 0.046875 + x = -0.377918332 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 = -0.377918332 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = -0.377918332 + -0.046875 x = -0.377918332 + -0.046875 Combine like terms: -0.377918332 + -0.046875 = -0.424793332 x = -0.424793332 Simplifying x = -0.424793332Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.331043332, -0.424793332}
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