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Simplifying 9x(7x + -8) = 92 Reorder the terms: 9x(-8 + 7x) = 92 (-8 * 9x + 7x * 9x) = 92 (-72x + 63x2) = 92 Solving -72x + 63x2 = 92 Solving for variable 'x'. Reorder the terms: -92 + -72x + 63x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + -72x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -1.46031746 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '1.46031746' to each side of the equation. -1.46031746 + -1.142857143x + 1.46031746 + x2 = 0 + 1.46031746 Reorder the terms: -1.46031746 + 1.46031746 + -1.142857143x + x2 = 0 + 1.46031746 Combine like terms: -1.46031746 + 1.46031746 = 0.00000000 0.00000000 + -1.142857143x + x2 = 0 + 1.46031746 -1.142857143x + x2 = 0 + 1.46031746 Combine like terms: 0 + 1.46031746 = 1.46031746 -1.142857143x + x2 = 1.46031746 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 1.46031746 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 1.46031746 + 0.3265306123 Combine like terms: 1.46031746 + 0.3265306123 = 1.7868480723 0.3265306123 + -1.142857143x + x2 = 1.7868480723 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.7868480723 Calculate the square root of the right side: 1.336730366 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.336730366 and -1.336730366.Subproblem 1
x + -0.5714285715 = 1.336730366 Simplifying x + -0.5714285715 = 1.336730366 Reorder the terms: -0.5714285715 + x = 1.336730366 Solving -0.5714285715 + x = 1.336730366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 1.336730366 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.336730366 + 0.5714285715 x = 1.336730366 + 0.5714285715 Combine like terms: 1.336730366 + 0.5714285715 = 1.9081589375 x = 1.9081589375 Simplifying x = 1.9081589375Subproblem 2
x + -0.5714285715 = -1.336730366 Simplifying x + -0.5714285715 = -1.336730366 Reorder the terms: -0.5714285715 + x = -1.336730366 Solving -0.5714285715 + x = -1.336730366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -1.336730366 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.336730366 + 0.5714285715 x = -1.336730366 + 0.5714285715 Combine like terms: -1.336730366 + 0.5714285715 = -0.7653017945 x = -0.7653017945 Simplifying x = -0.7653017945Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9081589375, -0.7653017945}
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