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Simplifying x = x2 + -14x + 10 Reorder the terms: x = 10 + -14x + x2 Solving x = 10 + -14x + x2 Solving for variable 'x'. Reorder the terms: -10 + x + 14x + -1x2 = 10 + -14x + x2 + -10 + 14x + -1x2 Combine like terms: x + 14x = 15x -10 + 15x + -1x2 = 10 + -14x + x2 + -10 + 14x + -1x2 Reorder the terms: -10 + 15x + -1x2 = 10 + -10 + -14x + 14x + x2 + -1x2 Combine like terms: 10 + -10 = 0 -10 + 15x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -10 + 15x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -10 + 15x + -1x2 = 0 + x2 + -1x2 -10 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -15x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -15x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -15x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -15x + x2 = 0 + -10 -15x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -15x + x2 = -10 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -10 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -10 + 56.25 Combine like terms: -10 + 56.25 = 46.25 56.25 + -15x + x2 = 46.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -7.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -7.5 = 6.800735254 Simplifying x + -7.5 = 6.800735254 Reorder the terms: -7.5 + x = 6.800735254 Solving -7.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.800735254 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.800735254 + 7.5 x = 6.800735254 + 7.5 Combine like terms: 6.800735254 + 7.5 = 14.300735254 x = 14.300735254 Simplifying x = 14.300735254Subproblem 2
x + -7.5 = -6.800735254 Simplifying x + -7.5 = -6.800735254 Reorder the terms: -7.5 + x = -6.800735254 Solving -7.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.800735254 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.800735254 + 7.5 x = -6.800735254 + 7.5 Combine like terms: -6.800735254 + 7.5 = 0.699264746 x = 0.699264746 Simplifying x = 0.699264746Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.300735254, 0.699264746}
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