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Simplifying x2 + -14x + -75 = -8 Reorder the terms: -75 + -14x + x2 = -8 Solving -75 + -14x + x2 = -8 Solving for variable 'x'. Reorder the terms: -75 + 8 + -14x + x2 = -8 + 8 Combine like terms: -75 + 8 = -67 -67 + -14x + x2 = -8 + 8 Combine like terms: -8 + 8 = 0 -67 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + -14x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -14x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -14x + x2 = 0 + 67 -14x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -14x + x2 = 67 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 = 67 + 49 Reorder the terms: 49 + -14x + x2 = 67 + 49 Combine like terms: 67 + 49 = 116 49 + -14x + x2 = 116 Factor a perfect square on the left side: (x + -7)(x + -7) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + -7) equal to 10.770329614 and -10.770329614.Subproblem 1
x + -7 = 10.770329614 Simplifying x + -7 = 10.770329614 Reorder the terms: -7 + x = 10.770329614 Solving -7 + x = 10.770329614 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 = 10.770329614 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.770329614 + 7 x = 10.770329614 + 7 Combine like terms: 10.770329614 + 7 = 17.770329614 x = 17.770329614 Simplifying x = 17.770329614Subproblem 2
x + -7 = -10.770329614 Simplifying x + -7 = -10.770329614 Reorder the terms: -7 + x = -10.770329614 Solving -7 + x = -10.770329614 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 = -10.770329614 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.770329614 + 7 x = -10.770329614 + 7 Combine like terms: -10.770329614 + 7 = -3.770329614 x = -3.770329614 Simplifying x = -3.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.770329614, -3.770329614}
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