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Simplifying 2x2 + -9 = 16x Reorder the terms: -9 + 2x2 = 16x Solving -9 + 2x2 = 16x Solving for variable 'x'. Reorder the terms: -9 + -16x + 2x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -9 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -8x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -8x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -8x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -8x + x2 = 0 + 4.5 -8x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -8x + x2 = 4.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 4.5 + 16 Reorder the terms: 16 + -8x + x2 = 4.5 + 16 Combine like terms: 4.5 + 16 = 20.5 16 + -8x + x2 = 20.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (x + -4) equal to 4.527692569 and -4.527692569.Subproblem 1
x + -4 = 4.527692569 Simplifying x + -4 = 4.527692569 Reorder the terms: -4 + x = 4.527692569 Solving -4 + x = 4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.527692569 + 4 x = 4.527692569 + 4 Combine like terms: 4.527692569 + 4 = 8.527692569 x = 8.527692569 Simplifying x = 8.527692569Subproblem 2
x + -4 = -4.527692569 Simplifying x + -4 = -4.527692569 Reorder the terms: -4 + x = -4.527692569 Solving -4 + x = -4.527692569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.527692569 + 4 x = -4.527692569 + 4 Combine like terms: -4.527692569 + 4 = -0.527692569 x = -0.527692569 Simplifying x = -0.527692569Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.527692569, -0.527692569}
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