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Simplifying 0 = 7x2 + -8x + -6 Reorder the terms: 0 = -6 + -8x + 7x2 Solving 0 = -6 + -8x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 6 = 6 6 + 8x + -7x2 = -6 + -8x + 7x2 + 6 + 8x + -7x2 Reorder the terms: 6 + 8x + -7x2 = -6 + 6 + -8x + 8x + 7x2 + -7x2 Combine like terms: -6 + 6 = 0 6 + 8x + -7x2 = 0 + -8x + 8x + 7x2 + -7x2 6 + 8x + -7x2 = -8x + 8x + 7x2 + -7x2 Combine like terms: -8x + 8x = 0 6 + 8x + -7x2 = 0 + 7x2 + -7x2 6 + 8x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 6 + 8x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1.142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1.142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.8571428571 -1.142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1.142857143x + x2 = 0.8571428571 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 = 0.8571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.8571428571 + 0.3265306123 Combine like terms: 0.8571428571 + 0.3265306123 = 1.1836734694 0.3265306123 + -1.142857143x + x2 = 1.1836734694 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 1.1836734694 Calculate the square root of the right side: 1.087967587 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.087967587 and -1.087967587.Subproblem 1
x + -0.5714285715 = 1.087967587 Simplifying x + -0.5714285715 = 1.087967587 Reorder the terms: -0.5714285715 + x = 1.087967587 Solving -0.5714285715 + x = 1.087967587 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 = 1.087967587 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.087967587 + 0.5714285715 x = 1.087967587 + 0.5714285715 Combine like terms: 1.087967587 + 0.5714285715 = 1.6593961585 x = 1.6593961585 Simplifying x = 1.6593961585Subproblem 2
x + -0.5714285715 = -1.087967587 Simplifying x + -0.5714285715 = -1.087967587 Reorder the terms: -0.5714285715 + x = -1.087967587 Solving -0.5714285715 + x = -1.087967587 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 = -1.087967587 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.087967587 + 0.5714285715 x = -1.087967587 + 0.5714285715 Combine like terms: -1.087967587 + 0.5714285715 = -0.5165390155 x = -0.5165390155 Simplifying x = -0.5165390155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6593961585, -0.5165390155}
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