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Simplifying 2x2 + 8x = 77 Reorder the terms: 8x + 2x2 = 77 Solving 8x + 2x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + 8x + 2x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -38.5 + 4x + x2 = 0 Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + 4x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + 4x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + 4x + x2 = 0 + 38.5 4x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 4x + x2 = 38.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 38.5 + 4 Reorder the terms: 4 + 4x + x2 = 38.5 + 4 Combine like terms: 38.5 + 4 = 42.5 4 + 4x + x2 = 42.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 42.5 Calculate the square root of the right side: 6.519202405 Break this problem into two subproblems by setting (x + 2) equal to 6.519202405 and -6.519202405.Subproblem 1
x + 2 = 6.519202405 Simplifying x + 2 = 6.519202405 Reorder the terms: 2 + x = 6.519202405 Solving 2 + x = 6.519202405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.519202405 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.519202405 + -2 x = 6.519202405 + -2 Combine like terms: 6.519202405 + -2 = 4.519202405 x = 4.519202405 Simplifying x = 4.519202405Subproblem 2
x + 2 = -6.519202405 Simplifying x + 2 = -6.519202405 Reorder the terms: 2 + x = -6.519202405 Solving 2 + x = -6.519202405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.519202405 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.519202405 + -2 x = -6.519202405 + -2 Combine like terms: -6.519202405 + -2 = -8.519202405 x = -8.519202405 Simplifying x = -8.519202405Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.519202405, -8.519202405}
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