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Simplifying x(12x + -84) = -113 Reorder the terms: x(-84 + 12x) = -113 (-84 * x + 12x * x) = -113 (-84x + 12x2) = -113 Solving -84x + 12x2 = -113 Solving for variable 'x'. Reorder the terms: 113 + -84x + 12x2 = -113 + 113 Combine like terms: -113 + 113 = 0 113 + -84x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 9.416666667 + -7x + x2 = 0 Move the constant term to the right: Add '-9.416666667' to each side of the equation. 9.416666667 + -7x + -9.416666667 + x2 = 0 + -9.416666667 Reorder the terms: 9.416666667 + -9.416666667 + -7x + x2 = 0 + -9.416666667 Combine like terms: 9.416666667 + -9.416666667 = 0.000000000 0.000000000 + -7x + x2 = 0 + -9.416666667 -7x + x2 = 0 + -9.416666667 Combine like terms: 0 + -9.416666667 = -9.416666667 -7x + x2 = -9.416666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -9.416666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -9.416666667 + 12.25 Combine like terms: -9.416666667 + 12.25 = 2.833333333 12.25 + -7x + x2 = 2.833333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 2.833333333 Calculate the square root of the right side: 1.683250823 Break this problem into two subproblems by setting (x + -3.5) equal to 1.683250823 and -1.683250823.Subproblem 1
x + -3.5 = 1.683250823 Simplifying x + -3.5 = 1.683250823 Reorder the terms: -3.5 + x = 1.683250823 Solving -3.5 + x = 1.683250823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.683250823 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.683250823 + 3.5 x = 1.683250823 + 3.5 Combine like terms: 1.683250823 + 3.5 = 5.183250823 x = 5.183250823 Simplifying x = 5.183250823Subproblem 2
x + -3.5 = -1.683250823 Simplifying x + -3.5 = -1.683250823 Reorder the terms: -3.5 + x = -1.683250823 Solving -3.5 + x = -1.683250823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.683250823 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.683250823 + 3.5 x = -1.683250823 + 3.5 Combine like terms: -1.683250823 + 3.5 = 1.816749177 x = 1.816749177 Simplifying x = 1.816749177Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.183250823, 1.816749177}
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