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Simplifying 0 = -7x2 + 8x + 3 Reorder the terms: 0 = 3 + 8x + -7x2 Solving 0 = 3 + 8x + -7x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -8x + 7x2 = 3 + 8x + -7x2 + -3 + -8x + 7x2 Reorder the terms: -3 + -8x + 7x2 = 3 + -3 + 8x + -8x + -7x2 + 7x2 Combine like terms: 3 + -3 = 0 -3 + -8x + 7x2 = 0 + 8x + -8x + -7x2 + 7x2 -3 + -8x + 7x2 = 8x + -8x + -7x2 + 7x2 Combine like terms: 8x + -8x = 0 -3 + -8x + 7x2 = 0 + -7x2 + 7x2 -3 + -8x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -3 + -8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.4285714286 -1.142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.142857143x + x2 = 0.4285714286 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 = 0.4285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.4285714286 + 0.3265306123 Combine like terms: 0.4285714286 + 0.3265306123 = 0.7551020409 0.3265306123 + -1.142857143x + x2 = 0.7551020409 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.7551020409 Calculate the square root of the right side: 0.868966076 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.868966076 and -0.868966076.Subproblem 1
x + -0.5714285715 = 0.868966076 Simplifying x + -0.5714285715 = 0.868966076 Reorder the terms: -0.5714285715 + x = 0.868966076 Solving -0.5714285715 + x = 0.868966076 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 = 0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.868966076 + 0.5714285715 x = 0.868966076 + 0.5714285715 Combine like terms: 0.868966076 + 0.5714285715 = 1.4403946475 x = 1.4403946475 Simplifying x = 1.4403946475Subproblem 2
x + -0.5714285715 = -0.868966076 Simplifying x + -0.5714285715 = -0.868966076 Reorder the terms: -0.5714285715 + x = -0.868966076 Solving -0.5714285715 + x = -0.868966076 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 = -0.868966076 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.868966076 + 0.5714285715 x = -0.868966076 + 0.5714285715 Combine like terms: -0.868966076 + 0.5714285715 = -0.2975375045 x = -0.2975375045 Simplifying x = -0.2975375045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4403946475, -0.2975375045}
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