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Simplifying 0.5x2 + -8x + 3 = 0 Reorder the terms: 3 + -8x + 0.5x2 = 0 Solving 3 + -8x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 6 + -16x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -16x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -16x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -16x + x2 = 0 + -6 -16x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -16x + x2 = -6 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -6 + 64 Reorder the terms: 64 + -16x + x2 = -6 + 64 Combine like terms: -6 + 64 = 58 64 + -16x + x2 = 58 Factor a perfect square on the left side: (x + -8)(x + -8) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -8) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -8 = 7.615773106 Simplifying x + -8 = 7.615773106 Reorder the terms: -8 + x = 7.615773106 Solving -8 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.615773106 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.615773106 + 8 x = 7.615773106 + 8 Combine like terms: 7.615773106 + 8 = 15.615773106 x = 15.615773106 Simplifying x = 15.615773106Subproblem 2
x + -8 = -7.615773106 Simplifying x + -8 = -7.615773106 Reorder the terms: -8 + x = -7.615773106 Solving -8 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.615773106 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.615773106 + 8 x = -7.615773106 + 8 Combine like terms: -7.615773106 + 8 = 0.384226894 x = 0.384226894 Simplifying x = 0.384226894Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.615773106, 0.384226894}
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