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Simplifying x2 + -10x + 25 = 19 Reorder the terms: 25 + -10x + x2 = 19 Solving 25 + -10x + x2 = 19 Solving for variable 'x'. Reorder the terms: 25 + -19 + -10x + x2 = 19 + -19 Combine like terms: 25 + -19 = 6 6 + -10x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 6 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -10x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -10x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -10x + x2 = 0 + -6 -10x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -10x + x2 = -6 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -6 + 25 Reorder the terms: 25 + -10x + x2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + -10x + x2 = 19 Factor a perfect square on the left side: (x + -5)(x + -5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -5) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -5 = 4.358898944 Simplifying x + -5 = 4.358898944 Reorder the terms: -5 + x = 4.358898944 Solving -5 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.358898944 + 5 x = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 x = 9.358898944 Simplifying x = 9.358898944Subproblem 2
x + -5 = -4.358898944 Simplifying x + -5 = -4.358898944 Reorder the terms: -5 + x = -4.358898944 Solving -5 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.358898944 + 5 x = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 x = 0.641101056 Simplifying x = 0.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.358898944, 0.641101056}
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