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Simplifying x2 + -14x + 49 = 19 Reorder the terms: 49 + -14x + x2 = 19 Solving 49 + -14x + x2 = 19 Solving for variable 'x'. Reorder the terms: 49 + -19 + -14x + x2 = 19 + -19 Combine like terms: 49 + -19 = 30 30 + -14x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 30 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -14x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -14x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -14x + x2 = 0 + -30 -14x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -14x + x2 = -30 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 = -30 + 49 Reorder the terms: 49 + -14x + x2 = -30 + 49 Combine like terms: -30 + 49 = 19 49 + -14x + x2 = 19 Factor a perfect square on the left side: (x + -7)(x + -7) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -7) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -7 = 4.358898944 Simplifying x + -7 = 4.358898944 Reorder the terms: -7 + x = 4.358898944 Solving -7 + x = 4.358898944 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 = 4.358898944 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.358898944 + 7 x = 4.358898944 + 7 Combine like terms: 4.358898944 + 7 = 11.358898944 x = 11.358898944 Simplifying x = 11.358898944Subproblem 2
x + -7 = -4.358898944 Simplifying x + -7 = -4.358898944 Reorder the terms: -7 + x = -4.358898944 Solving -7 + x = -4.358898944 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 = -4.358898944 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.358898944 + 7 x = -4.358898944 + 7 Combine like terms: -4.358898944 + 7 = 2.641101056 x = 2.641101056 Simplifying x = 2.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.358898944, 2.641101056}
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