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Simplifying 2x2 + 6x + 9 = 256 Reorder the terms: 9 + 6x + 2x2 = 256 Solving 9 + 6x + 2x2 = 256 Solving for variable 'x'. Reorder the terms: 9 + -256 + 6x + 2x2 = 256 + -256 Combine like terms: 9 + -256 = -247 -247 + 6x + 2x2 = 256 + -256 Combine like terms: 256 + -256 = 0 -247 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -123.5 + 3x + x2 = 0 Move the constant term to the right: Add '123.5' to each side of the equation. -123.5 + 3x + 123.5 + x2 = 0 + 123.5 Reorder the terms: -123.5 + 123.5 + 3x + x2 = 0 + 123.5 Combine like terms: -123.5 + 123.5 = 0.0 0.0 + 3x + x2 = 0 + 123.5 3x + x2 = 0 + 123.5 Combine like terms: 0 + 123.5 = 123.5 3x + x2 = 123.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 123.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 123.5 + 2.25 Combine like terms: 123.5 + 2.25 = 125.75 2.25 + 3x + x2 = 125.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 125.75 Calculate the square root of the right side: 11.213830746 Break this problem into two subproblems by setting (x + 1.5) equal to 11.213830746 and -11.213830746.Subproblem 1
x + 1.5 = 11.213830746 Simplifying x + 1.5 = 11.213830746 Reorder the terms: 1.5 + x = 11.213830746 Solving 1.5 + x = 11.213830746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.213830746 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.213830746 + -1.5 x = 11.213830746 + -1.5 Combine like terms: 11.213830746 + -1.5 = 9.713830746 x = 9.713830746 Simplifying x = 9.713830746Subproblem 2
x + 1.5 = -11.213830746 Simplifying x + 1.5 = -11.213830746 Reorder the terms: 1.5 + x = -11.213830746 Solving 1.5 + x = -11.213830746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.213830746 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.213830746 + -1.5 x = -11.213830746 + -1.5 Combine like terms: -11.213830746 + -1.5 = -12.713830746 x = -12.713830746 Simplifying x = -12.713830746Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.713830746, -12.713830746}
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