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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 = -83 -83 + -14x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -83 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '83' to each side of the equation. -83 + -14x + 83 + x2 = 0 + 83 Reorder the terms: -83 + 83 + -14x + x2 = 0 + 83 Combine like terms: -83 + 83 = 0 0 + -14x + x2 = 0 + 83 -14x + x2 = 0 + 83 Combine like terms: 0 + 83 = 83 -14x + x2 = 83 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 = 83 + 49 Reorder the terms: 49 + -14x + x2 = 83 + 49 Combine like terms: 83 + 49 = 132 49 + -14x + x2 = 132 Factor a perfect square on the left side: (x + -7)(x + -7) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -7) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -7 = 11.489125293 Simplifying x + -7 = 11.489125293 Reorder the terms: -7 + x = 11.489125293 Solving -7 + x = 11.489125293 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 = 11.489125293 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.489125293 + 7 x = 11.489125293 + 7 Combine like terms: 11.489125293 + 7 = 18.489125293 x = 18.489125293 Simplifying x = 18.489125293Subproblem 2
x + -7 = -11.489125293 Simplifying x + -7 = -11.489125293 Reorder the terms: -7 + x = -11.489125293 Solving -7 + x = -11.489125293 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 = -11.489125293 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.489125293 + 7 x = -11.489125293 + 7 Combine like terms: -11.489125293 + 7 = -4.489125293 x = -4.489125293 Simplifying x = -4.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.489125293, -4.489125293}
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