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Simplifying x2 + 14x = 10 Reorder the terms: 14x + x2 = 10 Solving 14x + x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 14x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 14x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 14x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 14x + x2 = 0 + 10 14x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 14x + x2 = 10 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 = 10 + 49 Reorder the terms: 49 + 14x + x2 = 10 + 49 Combine like terms: 10 + 49 = 59 49 + 14x + x2 = 59 Factor a perfect square on the left side: (x + 7)(x + 7) = 59 Calculate the square root of the right side: 7.681145748 Break this problem into two subproblems by setting (x + 7) equal to 7.681145748 and -7.681145748.Subproblem 1
x + 7 = 7.681145748 Simplifying x + 7 = 7.681145748 Reorder the terms: 7 + x = 7.681145748 Solving 7 + x = 7.681145748 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 = 7.681145748 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.681145748 + -7 x = 7.681145748 + -7 Combine like terms: 7.681145748 + -7 = 0.681145748 x = 0.681145748 Simplifying x = 0.681145748Subproblem 2
x + 7 = -7.681145748 Simplifying x + 7 = -7.681145748 Reorder the terms: 7 + x = -7.681145748 Solving 7 + x = -7.681145748 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 = -7.681145748 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.681145748 + -7 x = -7.681145748 + -7 Combine like terms: -7.681145748 + -7 = -14.681145748 x = -14.681145748 Simplifying x = -14.681145748Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.681145748, -14.681145748}
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