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Simplifying 8 + -2x2 + 13x = 0 Reorder the terms: 8 + 13x + -2x2 = 0 Solving 8 + 13x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4 + -6.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -6.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6.5x + x2 = 0 + 4 -6.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6.5x + x2 = 4 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 4 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 4 + 10.5625 Combine like terms: 4 + 10.5625 = 14.5625 10.5625 + -6.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -3.25) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -3.25 = 3.816084381 Simplifying x + -3.25 = 3.816084381 Reorder the terms: -3.25 + x = 3.816084381 Solving -3.25 + x = 3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.816084381 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.816084381 + 3.25 x = 3.816084381 + 3.25 Combine like terms: 3.816084381 + 3.25 = 7.066084381 x = 7.066084381 Simplifying x = 7.066084381Subproblem 2
x + -3.25 = -3.816084381 Simplifying x + -3.25 = -3.816084381 Reorder the terms: -3.25 + x = -3.816084381 Solving -3.25 + x = -3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.816084381 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.816084381 + 3.25 x = -3.816084381 + 3.25 Combine like terms: -3.816084381 + 3.25 = -0.566084381 x = -0.566084381 Simplifying x = -0.566084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.066084381, -0.566084381}
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