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Simplifying X(X + -14) = -43 Reorder the terms: X(-14 + X) = -43 (-14 * X + X * X) = -43 (-14X + X2) = -43 Solving -14X + X2 = -43 Solving for variable 'X'. Reorder the terms: 43 + -14X + X2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + -14X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -14X + -43 + X2 = 0 + -43 Reorder the terms: 43 + -43 + -14X + X2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -14X + X2 = 0 + -43 -14X + X2 = 0 + -43 Combine like terms: 0 + -43 = -43 -14X + X2 = -43 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 = -43 + 49 Reorder the terms: 49 + -14X + X2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + -14X + X2 = 6 Factor a perfect square on the left side: (X + -7)(X + -7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (X + -7) equal to 2.449489743 and -2.449489743.Subproblem 1
X + -7 = 2.449489743 Simplifying X + -7 = 2.449489743 Reorder the terms: -7 + X = 2.449489743 Solving -7 + X = 2.449489743 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 = 2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + X = 2.449489743 + 7 X = 2.449489743 + 7 Combine like terms: 2.449489743 + 7 = 9.449489743 X = 9.449489743 Simplifying X = 9.449489743Subproblem 2
X + -7 = -2.449489743 Simplifying X + -7 = -2.449489743 Reorder the terms: -7 + X = -2.449489743 Solving -7 + X = -2.449489743 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 = -2.449489743 + 7 Combine like terms: -7 + 7 = 0 0 + X = -2.449489743 + 7 X = -2.449489743 + 7 Combine like terms: -2.449489743 + 7 = 4.550510257 X = 4.550510257 Simplifying X = 4.550510257Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.449489743, 4.550510257}
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