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Simplifying 2x2 + -72 = 8x + 45 Reorder the terms: -72 + 2x2 = 8x + 45 Reorder the terms: -72 + 2x2 = 45 + 8x Solving -72 + 2x2 = 45 + 8x Solving for variable 'x'. Reorder the terms: -72 + -45 + -8x + 2x2 = 45 + 8x + -45 + -8x Combine like terms: -72 + -45 = -117 -117 + -8x + 2x2 = 45 + 8x + -45 + -8x Reorder the terms: -117 + -8x + 2x2 = 45 + -45 + 8x + -8x Combine like terms: 45 + -45 = 0 -117 + -8x + 2x2 = 0 + 8x + -8x -117 + -8x + 2x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -117 + -8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -58.5 + -4x + x2 = 0 Move the constant term to the right: Add '58.5' to each side of the equation. -58.5 + -4x + 58.5 + x2 = 0 + 58.5 Reorder the terms: -58.5 + 58.5 + -4x + x2 = 0 + 58.5 Combine like terms: -58.5 + 58.5 = 0.0 0.0 + -4x + x2 = 0 + 58.5 -4x + x2 = 0 + 58.5 Combine like terms: 0 + 58.5 = 58.5 -4x + x2 = 58.5 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 = 58.5 + 4 Reorder the terms: 4 + -4x + x2 = 58.5 + 4 Combine like terms: 58.5 + 4 = 62.5 4 + -4x + x2 = 62.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + -2) equal to 7.90569415 and -7.90569415.Subproblem 1
x + -2 = 7.90569415 Simplifying x + -2 = 7.90569415 Reorder the terms: -2 + x = 7.90569415 Solving -2 + x = 7.90569415 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 = 7.90569415 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.90569415 + 2 x = 7.90569415 + 2 Combine like terms: 7.90569415 + 2 = 9.90569415 x = 9.90569415 Simplifying x = 9.90569415Subproblem 2
x + -2 = -7.90569415 Simplifying x + -2 = -7.90569415 Reorder the terms: -2 + x = -7.90569415 Solving -2 + x = -7.90569415 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 = -7.90569415 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.90569415 + 2 x = -7.90569415 + 2 Combine like terms: -7.90569415 + 2 = -5.90569415 x = -5.90569415 Simplifying x = -5.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.90569415, -5.90569415}
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