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Simplifying x(x + -14) = 250 Reorder the terms: x(-14 + x) = 250 (-14 * x + x * x) = 250 (-14x + x2) = 250 Solving -14x + x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + -14x + x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + -14x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -14x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -14x + x2 = 0 + 250 -14x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -14x + x2 = 250 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 = 250 + 49 Reorder the terms: 49 + -14x + x2 = 250 + 49 Combine like terms: 250 + 49 = 299 49 + -14x + x2 = 299 Factor a perfect square on the left side: (x + -7)(x + -7) = 299 Calculate the square root of the right side: 17.291616466 Break this problem into two subproblems by setting (x + -7) equal to 17.291616466 and -17.291616466.Subproblem 1
x + -7 = 17.291616466 Simplifying x + -7 = 17.291616466 Reorder the terms: -7 + x = 17.291616466 Solving -7 + x = 17.291616466 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 = 17.291616466 + 7 Combine like terms: -7 + 7 = 0 0 + x = 17.291616466 + 7 x = 17.291616466 + 7 Combine like terms: 17.291616466 + 7 = 24.291616466 x = 24.291616466 Simplifying x = 24.291616466Subproblem 2
x + -7 = -17.291616466 Simplifying x + -7 = -17.291616466 Reorder the terms: -7 + x = -17.291616466 Solving -7 + x = -17.291616466 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 = -17.291616466 + 7 Combine like terms: -7 + 7 = 0 0 + x = -17.291616466 + 7 x = -17.291616466 + 7 Combine like terms: -17.291616466 + 7 = -10.291616466 x = -10.291616466 Simplifying x = -10.291616466Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.291616466, -10.291616466}
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