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Simplifying 8x(6x + 5) = 1 Reorder the terms: 8x(5 + 6x) = 1 (5 * 8x + 6x * 8x) = 1 (40x + 48x2) = 1 Solving 40x + 48x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 40x + 48x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 40x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.02083333333 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.02083333333' to each side of the equation. -0.02083333333 + 0.8333333333x + 0.02083333333 + x2 = 0 + 0.02083333333 Reorder the terms: -0.02083333333 + 0.02083333333 + 0.8333333333x + x2 = 0 + 0.02083333333 Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000 0.00000000000 + 0.8333333333x + x2 = 0 + 0.02083333333 0.8333333333x + x2 = 0 + 0.02083333333 Combine like terms: 0 + 0.02083333333 = 0.02083333333 0.8333333333x + x2 = 0.02083333333 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 0.02083333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 0.02083333333 + 0.1736111111 Combine like terms: 0.02083333333 + 0.1736111111 = 0.19444444443 0.1736111111 + 0.8333333333x + x2 = 0.19444444443 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 0.19444444443 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 0.440958552 and -0.440958552.Subproblem 1
x + 0.4166666667 = 0.440958552 Simplifying x + 0.4166666667 = 0.440958552 Reorder the terms: 0.4166666667 + x = 0.440958552 Solving 0.4166666667 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.440958552 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.440958552 + -0.4166666667 x = 0.440958552 + -0.4166666667 Combine like terms: 0.440958552 + -0.4166666667 = 0.0242918853 x = 0.0242918853 Simplifying x = 0.0242918853Subproblem 2
x + 0.4166666667 = -0.440958552 Simplifying x + 0.4166666667 = -0.440958552 Reorder the terms: 0.4166666667 + x = -0.440958552 Solving 0.4166666667 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.440958552 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.440958552 + -0.4166666667 x = -0.440958552 + -0.4166666667 Combine like terms: -0.440958552 + -0.4166666667 = -0.8576252187 x = -0.8576252187 Simplifying x = -0.8576252187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0242918853, -0.8576252187}
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