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Simplifying x2 + -14x = 9 Reorder the terms: -14x + x2 = 9 Solving -14x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -14x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -14x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -14x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14x + x2 = 0 + 9 -14x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -14x + x2 = 9 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 = 9 + 49 Reorder the terms: 49 + -14x + x2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + -14x + x2 = 58 Factor a perfect square on the left side: (x + -7)(x + -7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (x + -7) equal to 7.615773106 and -7.615773106.Subproblem 1
x + -7 = 7.615773106 Simplifying x + -7 = 7.615773106 Reorder the terms: -7 + x = 7.615773106 Solving -7 + x = 7.615773106 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 = 7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.615773106 + 7 x = 7.615773106 + 7 Combine like terms: 7.615773106 + 7 = 14.615773106 x = 14.615773106 Simplifying x = 14.615773106Subproblem 2
x + -7 = -7.615773106 Simplifying x + -7 = -7.615773106 Reorder the terms: -7 + x = -7.615773106 Solving -7 + x = -7.615773106 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 = -7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.615773106 + 7 x = -7.615773106 + 7 Combine like terms: -7.615773106 + 7 = -0.615773106 x = -0.615773106 Simplifying x = -0.615773106Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.615773106, -0.615773106}
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