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Simplifying 7x2 + 8x + 1 = 100 Reorder the terms: 1 + 8x + 7x2 = 100 Solving 1 + 8x + 7x2 = 100 Solving for variable 'x'. Reorder the terms: 1 + -100 + 8x + 7x2 = 100 + -100 Combine like terms: 1 + -100 = -99 -99 + 8x + 7x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -99 + 8x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -14.14285714 + 1.142857143x + x2 = 0 Move the constant term to the right: Add '14.14285714' to each side of the equation. -14.14285714 + 1.142857143x + 14.14285714 + x2 = 0 + 14.14285714 Reorder the terms: -14.14285714 + 14.14285714 + 1.142857143x + x2 = 0 + 14.14285714 Combine like terms: -14.14285714 + 14.14285714 = 0.00000000 0.00000000 + 1.142857143x + x2 = 0 + 14.14285714 1.142857143x + x2 = 0 + 14.14285714 Combine like terms: 0 + 14.14285714 = 14.14285714 1.142857143x + x2 = 14.14285714 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 = 14.14285714 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143x + x2 = 14.14285714 + 0.3265306123 Combine like terms: 14.14285714 + 0.3265306123 = 14.4693877523 0.3265306123 + 1.142857143x + x2 = 14.4693877523 Factor a perfect square on the left side: (x + 0.5714285715)(x + 0.5714285715) = 14.4693877523 Calculate the square root of the right side: 3.803864844 Break this problem into two subproblems by setting (x + 0.5714285715) equal to 3.803864844 and -3.803864844.Subproblem 1
x + 0.5714285715 = 3.803864844 Simplifying x + 0.5714285715 = 3.803864844 Reorder the terms: 0.5714285715 + x = 3.803864844 Solving 0.5714285715 + x = 3.803864844 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 = 3.803864844 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = 3.803864844 + -0.5714285715 x = 3.803864844 + -0.5714285715 Combine like terms: 3.803864844 + -0.5714285715 = 3.2324362725 x = 3.2324362725 Simplifying x = 3.2324362725Subproblem 2
x + 0.5714285715 = -3.803864844 Simplifying x + 0.5714285715 = -3.803864844 Reorder the terms: 0.5714285715 + x = -3.803864844 Solving 0.5714285715 + x = -3.803864844 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 = -3.803864844 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + x = -3.803864844 + -0.5714285715 x = -3.803864844 + -0.5714285715 Combine like terms: -3.803864844 + -0.5714285715 = -4.3752934155 x = -4.3752934155 Simplifying x = -4.3752934155Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2324362725, -4.3752934155}
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