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Simplifying 0 = 0.5x2 + -6x + 7 Reorder the terms: 0 = 7 + -6x + 0.5x2 Solving 0 = 7 + -6x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + 6x + -0.5x2 = 7 + -6x + 0.5x2 + -7 + 6x + -0.5x2 Reorder the terms: -7 + 6x + -0.5x2 = 7 + -7 + -6x + 6x + 0.5x2 + -0.5x2 Combine like terms: 7 + -7 = 0 -7 + 6x + -0.5x2 = 0 + -6x + 6x + 0.5x2 + -0.5x2 -7 + 6x + -0.5x2 = -6x + 6x + 0.5x2 + -0.5x2 Combine like terms: -6x + 6x = 0 -7 + 6x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -7 + 6x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -7 + 6x + -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'. 14 + -12x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -12x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -12x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -12x + x2 = 0 + -14 -12x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -12x + x2 = -14 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -14 + 36 Reorder the terms: 36 + -12x + x2 = -14 + 36 Combine like terms: -14 + 36 = 22 36 + -12x + x2 = 22 Factor a perfect square on the left side: (x + -6)(x + -6) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -6) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -6 = 4.69041576 Simplifying x + -6 = 4.69041576 Reorder the terms: -6 + x = 4.69041576 Solving -6 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.69041576 + 6 x = 4.69041576 + 6 Combine like terms: 4.69041576 + 6 = 10.69041576 x = 10.69041576 Simplifying x = 10.69041576Subproblem 2
x + -6 = -4.69041576 Simplifying x + -6 = -4.69041576 Reorder the terms: -6 + x = -4.69041576 Solving -6 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.69041576 + 6 x = -4.69041576 + 6 Combine like terms: -4.69041576 + 6 = 1.30958424 x = 1.30958424 Simplifying x = 1.30958424Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.69041576, 1.30958424}
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