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Simplifying x2 + 19 = 14x Reorder the terms: 19 + x2 = 14x Solving 19 + x2 = 14x Solving for variable 'x'. Reorder the terms: 19 + -14x + x2 = 14x + -14x Combine like terms: 14x + -14x = 0 19 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -14x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14x + x2 = 0 + -19 -14x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14x + x2 = -19 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 = -19 + 49 Reorder the terms: 49 + -14x + x2 = -19 + 49 Combine like terms: -19 + 49 = 30 49 + -14x + x2 = 30 Factor a perfect square on the left side: (x + -7)(x + -7) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -7) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -7 = 5.477225575 Simplifying x + -7 = 5.477225575 Reorder the terms: -7 + x = 5.477225575 Solving -7 + x = 5.477225575 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 = 5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.477225575 + 7 x = 5.477225575 + 7 Combine like terms: 5.477225575 + 7 = 12.477225575 x = 12.477225575 Simplifying x = 12.477225575Subproblem 2
x + -7 = -5.477225575 Simplifying x + -7 = -5.477225575 Reorder the terms: -7 + x = -5.477225575 Solving -7 + x = -5.477225575 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 = -5.477225575 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.477225575 + 7 x = -5.477225575 + 7 Combine like terms: -5.477225575 + 7 = 1.522774425 x = 1.522774425 Simplifying x = 1.522774425Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.477225575, 1.522774425}
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