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Simplifying 8x(x + -1) = 7x + 20 Reorder the terms: 8x(-1 + x) = 7x + 20 (-1 * 8x + x * 8x) = 7x + 20 (-8x + 8x2) = 7x + 20 Reorder the terms: -8x + 8x2 = 20 + 7x Solving -8x + 8x2 = 20 + 7x Solving for variable 'x'. Reorder the terms: -20 + -8x + -7x + 8x2 = 20 + 7x + -20 + -7x Combine like terms: -8x + -7x = -15x -20 + -15x + 8x2 = 20 + 7x + -20 + -7x Reorder the terms: -20 + -15x + 8x2 = 20 + -20 + 7x + -7x Combine like terms: 20 + -20 = 0 -20 + -15x + 8x2 = 0 + 7x + -7x -20 + -15x + 8x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -20 + -15x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + -1.875x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.875x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.875x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.875x + x2 = 0 + 2.5 -1.875x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.875x + x2 = 2.5 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = 2.5 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = 2.5 + 0.87890625 Combine like terms: 2.5 + 0.87890625 = 3.37890625 0.87890625 + -1.875x + x2 = 3.37890625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 3.37890625 Calculate the square root of the right side: 1.838180146 Break this problem into two subproblems by setting (x + -0.9375) equal to 1.838180146 and -1.838180146.Subproblem 1
x + -0.9375 = 1.838180146 Simplifying x + -0.9375 = 1.838180146 Reorder the terms: -0.9375 + x = 1.838180146 Solving -0.9375 + x = 1.838180146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.838180146 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.838180146 + 0.9375 x = 1.838180146 + 0.9375 Combine like terms: 1.838180146 + 0.9375 = 2.775680146 x = 2.775680146 Simplifying x = 2.775680146Subproblem 2
x + -0.9375 = -1.838180146 Simplifying x + -0.9375 = -1.838180146 Reorder the terms: -0.9375 + x = -1.838180146 Solving -0.9375 + x = -1.838180146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.838180146 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.838180146 + 0.9375 x = -1.838180146 + 0.9375 Combine like terms: -1.838180146 + 0.9375 = -0.900680146 x = -0.900680146 Simplifying x = -0.900680146Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.775680146, -0.900680146}
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