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Simplifying 8(x * x) + -13x = 35 Multiply x * x 8(x2) + -13x = 35 Reorder the terms: -13x + 8x2 = 35 Solving -13x + 8x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -13x + 8x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -13x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + -1.625x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -1.625x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -1.625x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -1.625x + x2 = 0 + 4.375 -1.625x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -1.625x + x2 = 4.375 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = 4.375 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = 4.375 + 0.66015625 Combine like terms: 4.375 + 0.66015625 = 5.03515625 0.66015625 + -1.625x + x2 = 5.03515625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 5.03515625 Calculate the square root of the right side: 2.243915384 Break this problem into two subproblems by setting (x + -0.8125) equal to 2.243915384 and -2.243915384.Subproblem 1
x + -0.8125 = 2.243915384 Simplifying x + -0.8125 = 2.243915384 Reorder the terms: -0.8125 + x = 2.243915384 Solving -0.8125 + x = 2.243915384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 2.243915384 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 2.243915384 + 0.8125 x = 2.243915384 + 0.8125 Combine like terms: 2.243915384 + 0.8125 = 3.056415384 x = 3.056415384 Simplifying x = 3.056415384Subproblem 2
x + -0.8125 = -2.243915384 Simplifying x + -0.8125 = -2.243915384 Reorder the terms: -0.8125 + x = -2.243915384 Solving -0.8125 + x = -2.243915384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -2.243915384 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -2.243915384 + 0.8125 x = -2.243915384 + 0.8125 Combine like terms: -2.243915384 + 0.8125 = -1.431415384 x = -1.431415384 Simplifying x = -1.431415384Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.056415384, -1.431415384}
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