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Simplifying 0 = x2 + 8x + -225 Reorder the terms: 0 = -225 + 8x + x2 Solving 0 = -225 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 225 = 225 225 + -8x + -1x2 = -225 + 8x + x2 + 225 + -8x + -1x2 Reorder the terms: 225 + -8x + -1x2 = -225 + 225 + 8x + -8x + x2 + -1x2 Combine like terms: -225 + 225 = 0 225 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 225 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 225 + -8x + -1x2 = 0 + x2 + -1x2 225 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 225 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + 8x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + 8x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 8x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 8x + x2 = 0 + 225 8x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 8x + x2 = 225 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 = 225 + 16 Reorder the terms: 16 + 8x + x2 = 225 + 16 Combine like terms: 225 + 16 = 241 16 + 8x + x2 = 241 Factor a perfect square on the left side: (x + 4)(x + 4) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 4) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 4 = 15.524174696 Simplifying x + 4 = 15.524174696 Reorder the terms: 4 + x = 15.524174696 Solving 4 + x = 15.524174696 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 = 15.524174696 + -4 Combine like terms: 4 + -4 = 0 0 + x = 15.524174696 + -4 x = 15.524174696 + -4 Combine like terms: 15.524174696 + -4 = 11.524174696 x = 11.524174696 Simplifying x = 11.524174696Subproblem 2
x + 4 = -15.524174696 Simplifying x + 4 = -15.524174696 Reorder the terms: 4 + x = -15.524174696 Solving 4 + x = -15.524174696 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 = -15.524174696 + -4 Combine like terms: 4 + -4 = 0 0 + x = -15.524174696 + -4 x = -15.524174696 + -4 Combine like terms: -15.524174696 + -4 = -19.524174696 x = -19.524174696 Simplifying x = -19.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.524174696, -19.524174696}
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