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Simplifying 0 = 2x2 + -16x + 9 Reorder the terms: 0 = 9 + -16x + 2x2 Solving 0 = 9 + -16x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 16x + -2x2 = 9 + -16x + 2x2 + -9 + 16x + -2x2 Reorder the terms: -9 + 16x + -2x2 = 9 + -9 + -16x + 16x + 2x2 + -2x2 Combine like terms: 9 + -9 = 0 -9 + 16x + -2x2 = 0 + -16x + 16x + 2x2 + -2x2 -9 + 16x + -2x2 = -16x + 16x + 2x2 + -2x2 Combine like terms: -16x + 16x = 0 -9 + 16x + -2x2 = 0 + 2x2 + -2x2 -9 + 16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 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 = 11.5 16 + -8x + x2 = 11.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -4) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -4 = 3.391164992 Simplifying x + -4 = 3.391164992 Reorder the terms: -4 + x = 3.391164992 Solving -4 + x = 3.391164992 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 = 3.391164992 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.391164992 + 4 x = 3.391164992 + 4 Combine like terms: 3.391164992 + 4 = 7.391164992 x = 7.391164992 Simplifying x = 7.391164992Subproblem 2
x + -4 = -3.391164992 Simplifying x + -4 = -3.391164992 Reorder the terms: -4 + x = -3.391164992 Solving -4 + x = -3.391164992 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 = -3.391164992 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.391164992 + 4 x = -3.391164992 + 4 Combine like terms: -3.391164992 + 4 = 0.608835008 x = 0.608835008 Simplifying x = 0.608835008Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.391164992, 0.608835008}
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