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Simplifying 2x2 + 8x = 73 Reorder the terms: 8x + 2x2 = 73 Solving 8x + 2x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 8x + 2x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + 4x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + 4x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + 4x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + 4x + x2 = 0 + 36.5 4x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 4x + x2 = 36.5 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 = 36.5 + 4 Reorder the terms: 4 + 4x + x2 = 36.5 + 4 Combine like terms: 36.5 + 4 = 40.5 4 + 4x + x2 = 40.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (x + 2) equal to 6.363961031 and -6.363961031.Subproblem 1
x + 2 = 6.363961031 Simplifying x + 2 = 6.363961031 Reorder the terms: 2 + x = 6.363961031 Solving 2 + x = 6.363961031 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 = 6.363961031 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.363961031 + -2 x = 6.363961031 + -2 Combine like terms: 6.363961031 + -2 = 4.363961031 x = 4.363961031 Simplifying x = 4.363961031Subproblem 2
x + 2 = -6.363961031 Simplifying x + 2 = -6.363961031 Reorder the terms: 2 + x = -6.363961031 Solving 2 + x = -6.363961031 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 = -6.363961031 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.363961031 + -2 x = -6.363961031 + -2 Combine like terms: -6.363961031 + -2 = -8.363961031 x = -8.363961031 Simplifying x = -8.363961031Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.363961031, -8.363961031}
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