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Simplifying 2x2 + -18x + 31 = 0 Reorder the terms: 31 + -18x + 2x2 = 0 Solving 31 + -18x + 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'. 15.5 + -9x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + -9x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + -9x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + -9x + x2 = 0 + -15.5 -9x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 -9x + x2 = -15.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -15.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -15.5 + 20.25 Combine like terms: -15.5 + 20.25 = 4.75 20.25 + -9x + x2 = 4.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -4.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -4.5 = 2.179449472 Simplifying x + -4.5 = 2.179449472 Reorder the terms: -4.5 + x = 2.179449472 Solving -4.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 2.179449472 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.179449472 + 4.5 x = 2.179449472 + 4.5 Combine like terms: 2.179449472 + 4.5 = 6.679449472 x = 6.679449472 Simplifying x = 6.679449472Subproblem 2
x + -4.5 = -2.179449472 Simplifying x + -4.5 = -2.179449472 Reorder the terms: -4.5 + x = -2.179449472 Solving -4.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -2.179449472 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.179449472 + 4.5 x = -2.179449472 + 4.5 Combine like terms: -2.179449472 + 4.5 = 2.320550528 x = 2.320550528 Simplifying x = 2.320550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.679449472, 2.320550528}
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