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Simplifying 0 = x2 + -14x + -84 Reorder the terms: 0 = -84 + -14x + x2 Solving 0 = -84 + -14x + x2 Solving for variable 'x'. Combine like terms: 0 + 84 = 84 84 + 14x + -1x2 = -84 + -14x + x2 + 84 + 14x + -1x2 Reorder the terms: 84 + 14x + -1x2 = -84 + 84 + -14x + 14x + x2 + -1x2 Combine like terms: -84 + 84 = 0 84 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 84 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 84 + 14x + -1x2 = 0 + x2 + -1x2 84 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 84 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -84 + -14x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + -14x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -14x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -14x + x2 = 0 + 84 -14x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -14x + x2 = 84 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 = 84 + 49 Reorder the terms: 49 + -14x + x2 = 84 + 49 Combine like terms: 84 + 49 = 133 49 + -14x + x2 = 133 Factor a perfect square on the left side: (x + -7)(x + -7) = 133 Calculate the square root of the right side: 11.532562595 Break this problem into two subproblems by setting (x + -7) equal to 11.532562595 and -11.532562595.Subproblem 1
x + -7 = 11.532562595 Simplifying x + -7 = 11.532562595 Reorder the terms: -7 + x = 11.532562595 Solving -7 + x = 11.532562595 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 = 11.532562595 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.532562595 + 7 x = 11.532562595 + 7 Combine like terms: 11.532562595 + 7 = 18.532562595 x = 18.532562595 Simplifying x = 18.532562595Subproblem 2
x + -7 = -11.532562595 Simplifying x + -7 = -11.532562595 Reorder the terms: -7 + x = -11.532562595 Solving -7 + x = -11.532562595 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 = -11.532562595 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.532562595 + 7 x = -11.532562595 + 7 Combine like terms: -11.532562595 + 7 = -4.532562595 x = -4.532562595 Simplifying x = -4.532562595Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.532562595, -4.532562595}
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