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Simplifying 192 + -14x + -1x2 = 0 Solving 192 + -14x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -192 + 14x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 14x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 14x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 14x + x2 = 0 + 192 14x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 14x + x2 = 192 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 192 + 49 Reorder the terms: 49 + 14x + x2 = 192 + 49 Combine like terms: 192 + 49 = 241 49 + 14x + x2 = 241 Factor a perfect square on the left side: (x + 7)(x + 7) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + 7) equal to 15.524174696 and -15.524174696.Subproblem 1
x + 7 = 15.524174696 Simplifying x + 7 = 15.524174696 Reorder the terms: 7 + x = 15.524174696 Solving 7 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 15.524174696 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.524174696 + -7 x = 15.524174696 + -7 Combine like terms: 15.524174696 + -7 = 8.524174696 x = 8.524174696 Simplifying x = 8.524174696Subproblem 2
x + 7 = -15.524174696 Simplifying x + 7 = -15.524174696 Reorder the terms: 7 + x = -15.524174696 Solving 7 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -15.524174696 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.524174696 + -7 x = -15.524174696 + -7 Combine like terms: -15.524174696 + -7 = -22.524174696 x = -22.524174696 Simplifying x = -22.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.524174696, -22.524174696}
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