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Simplifying 7(6X + -1) * X = 36 Reorder the terms: 7(-1 + 6X) * X = 36 Reorder the terms for easier multiplication: 7X(-1 + 6X) = 36 (-1 * 7X + 6X * 7X) = 36 (-7X + 42X2) = 36 Solving -7X + 42X2 = 36 Solving for variable 'X'. Reorder the terms: -36 + -7X + 42X2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -7X + 42X2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.8571428571 + -0.1666666667X + X2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.1666666667X + 0.8571428571 + X2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.1666666667X + X2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.1666666667X + X2 = 0 + 0.8571428571 -0.1666666667X + X2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.1666666667X + X2 = 0.8571428571 The X term is -0.1666666667X. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667X + 0.006944444447 + X2 = 0.8571428571 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667X + X2 = 0.8571428571 + 0.006944444447 Combine like terms: 0.8571428571 + 0.006944444447 = 0.864087301547 0.006944444447 + -0.1666666667X + X2 = 0.864087301547 Factor a perfect square on the left side: (X + -0.08333333335)(X + -0.08333333335) = 0.864087301547 Calculate the square root of the right side: 0.929562963 Break this problem into two subproblems by setting (X + -0.08333333335) equal to 0.929562963 and -0.929562963.Subproblem 1
X + -0.08333333335 = 0.929562963 Simplifying X + -0.08333333335 = 0.929562963 Reorder the terms: -0.08333333335 + X = 0.929562963 Solving -0.08333333335 + X = 0.929562963 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + X = 0.929562963 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + X = 0.929562963 + 0.08333333335 X = 0.929562963 + 0.08333333335 Combine like terms: 0.929562963 + 0.08333333335 = 1.01289629635 X = 1.01289629635 Simplifying X = 1.01289629635Subproblem 2
X + -0.08333333335 = -0.929562963 Simplifying X + -0.08333333335 = -0.929562963 Reorder the terms: -0.08333333335 + X = -0.929562963 Solving -0.08333333335 + X = -0.929562963 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + X = -0.929562963 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + X = -0.929562963 + 0.08333333335 X = -0.929562963 + 0.08333333335 Combine like terms: -0.929562963 + 0.08333333335 = -0.84622962965 X = -0.84622962965 Simplifying X = -0.84622962965Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.01289629635, -0.84622962965}
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