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Simplifying 7(8x + 5) * x = 2 Reorder the terms: 7(5 + 8x) * x = 2 Reorder the terms for easier multiplication: 7x(5 + 8x) = 2 (5 * 7x + 8x * 7x) = 2 (35x + 56x2) = 2 Solving 35x + 56x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 35x + 56x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 35x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. -0.03571428571 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.03571428571' to each side of the equation. -0.03571428571 + 0.625x + 0.03571428571 + x2 = 0 + 0.03571428571 Reorder the terms: -0.03571428571 + 0.03571428571 + 0.625x + x2 = 0 + 0.03571428571 Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000 0.00000000000 + 0.625x + x2 = 0 + 0.03571428571 0.625x + x2 = 0 + 0.03571428571 Combine like terms: 0 + 0.03571428571 = 0.03571428571 0.625x + x2 = 0.03571428571 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 0.03571428571 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.03571428571 + 0.09765625 Combine like terms: 0.03571428571 + 0.09765625 = 0.13337053571 0.09765625 + 0.625x + x2 = 0.13337053571 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.13337053571 Calculate the square root of the right side: 0.36519931 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.36519931 and -0.36519931.Subproblem 1
x + 0.3125 = 0.36519931 Simplifying x + 0.3125 = 0.36519931 Reorder the terms: 0.3125 + x = 0.36519931 Solving 0.3125 + x = 0.36519931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 0.36519931 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.36519931 + -0.3125 x = 0.36519931 + -0.3125 Combine like terms: 0.36519931 + -0.3125 = 0.05269931 x = 0.05269931 Simplifying x = 0.05269931Subproblem 2
x + 0.3125 = -0.36519931 Simplifying x + 0.3125 = -0.36519931 Reorder the terms: 0.3125 + x = -0.36519931 Solving 0.3125 + x = -0.36519931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -0.36519931 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.36519931 + -0.3125 x = -0.36519931 + -0.3125 Combine like terms: -0.36519931 + -0.3125 = -0.67769931 x = -0.67769931 Simplifying x = -0.67769931Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.05269931, -0.67769931}
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