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Simplifying 8x2 + -30x + -25 = 0 Reorder the terms: -25 + -30x + 8x2 = 0 Solving -25 + -30x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + -3.75x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -3.75x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -3.75x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -3.75x + x2 = 0 + 3.125 -3.75x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -3.75x + x2 = 3.125 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 3.125 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 3.125 + 3.515625 Combine like terms: 3.125 + 3.515625 = 6.640625 3.515625 + -3.75x + x2 = 6.640625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + -1.875) equal to 2.576941016 and -2.576941016.Subproblem 1
x + -1.875 = 2.576941016 Simplifying x + -1.875 = 2.576941016 Reorder the terms: -1.875 + x = 2.576941016 Solving -1.875 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.576941016 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.576941016 + 1.875 x = 2.576941016 + 1.875 Combine like terms: 2.576941016 + 1.875 = 4.451941016 x = 4.451941016 Simplifying x = 4.451941016Subproblem 2
x + -1.875 = -2.576941016 Simplifying x + -1.875 = -2.576941016 Reorder the terms: -1.875 + x = -2.576941016 Solving -1.875 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.576941016 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.576941016 + 1.875 x = -2.576941016 + 1.875 Combine like terms: -2.576941016 + 1.875 = -0.701941016 x = -0.701941016 Simplifying x = -0.701941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.451941016, -0.701941016}
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