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Simplifying (8x + -7) * 6x = 73 Reorder the terms: (-7 + 8x) * 6x = 73 Reorder the terms for easier multiplication: 6x(-7 + 8x) = 73 (-7 * 6x + 8x * 6x) = 73 (-42x + 48x2) = 73 Solving -42x + 48x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + -42x + 48x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + -42x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -1.520833333 + -0.875x + x2 = 0 Move the constant term to the right: Add '1.520833333' to each side of the equation. -1.520833333 + -0.875x + 1.520833333 + x2 = 0 + 1.520833333 Reorder the terms: -1.520833333 + 1.520833333 + -0.875x + x2 = 0 + 1.520833333 Combine like terms: -1.520833333 + 1.520833333 = 0.000000000 0.000000000 + -0.875x + x2 = 0 + 1.520833333 -0.875x + x2 = 0 + 1.520833333 Combine like terms: 0 + 1.520833333 = 1.520833333 -0.875x + x2 = 1.520833333 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 1.520833333 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 1.520833333 + 0.19140625 Combine like terms: 1.520833333 + 0.19140625 = 1.712239583 0.19140625 + -0.875x + x2 = 1.712239583 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 1.712239583 Calculate the square root of the right side: 1.308525729 Break this problem into two subproblems by setting (x + -0.4375) equal to 1.308525729 and -1.308525729.Subproblem 1
x + -0.4375 = 1.308525729 Simplifying x + -0.4375 = 1.308525729 Reorder the terms: -0.4375 + x = 1.308525729 Solving -0.4375 + x = 1.308525729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 1.308525729 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 1.308525729 + 0.4375 x = 1.308525729 + 0.4375 Combine like terms: 1.308525729 + 0.4375 = 1.746025729 x = 1.746025729 Simplifying x = 1.746025729Subproblem 2
x + -0.4375 = -1.308525729 Simplifying x + -0.4375 = -1.308525729 Reorder the terms: -0.4375 + x = -1.308525729 Solving -0.4375 + x = -1.308525729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -1.308525729 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -1.308525729 + 0.4375 x = -1.308525729 + 0.4375 Combine like terms: -1.308525729 + 0.4375 = -0.871025729 x = -0.871025729 Simplifying x = -0.871025729Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.746025729, -0.871025729}
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