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Simplifying 0 = 0.5x2 + 2x + -9 Reorder the terms: 0 = -9 + 2x + 0.5x2 Solving 0 = -9 + 2x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -2x + -0.5x2 = -9 + 2x + 0.5x2 + 9 + -2x + -0.5x2 Reorder the terms: 9 + -2x + -0.5x2 = -9 + 9 + 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: -9 + 9 = 0 9 + -2x + -0.5x2 = 0 + 2x + -2x + 0.5x2 + -0.5x2 9 + -2x + -0.5x2 = 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: 2x + -2x = 0 9 + -2x + -0.5x2 = 0 + 0.5x2 + -0.5x2 9 + -2x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 9 + -2x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -18 + 4x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 4x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 4x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 4x + x2 = 0 + 18 4x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 4x + x2 = 18 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 = 18 + 4 Reorder the terms: 4 + 4x + x2 = 18 + 4 Combine like terms: 18 + 4 = 22 4 + 4x + x2 = 22 Factor a perfect square on the left side: (x + 2)(x + 2) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 2) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 2 = 4.69041576 Simplifying x + 2 = 4.69041576 Reorder the terms: 2 + x = 4.69041576 Solving 2 + x = 4.69041576 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 = 4.69041576 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.69041576 + -2 x = 4.69041576 + -2 Combine like terms: 4.69041576 + -2 = 2.69041576 x = 2.69041576 Simplifying x = 2.69041576Subproblem 2
x + 2 = -4.69041576 Simplifying x + 2 = -4.69041576 Reorder the terms: 2 + x = -4.69041576 Solving 2 + x = -4.69041576 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 = -4.69041576 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.69041576 + -2 x = -4.69041576 + -2 Combine like terms: -4.69041576 + -2 = -6.69041576 x = -6.69041576 Simplifying x = -6.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.69041576, -6.69041576}
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