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Simplifying (x + 7)(x + 7) = 10 Reorder the terms: (7 + x)(x + 7) = 10 Reorder the terms: (7 + x)(7 + x) = 10 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) = 10 ((7 * 7 + x * 7) + x(7 + x)) = 10 ((49 + 7x) + x(7 + x)) = 10 (49 + 7x + (7 * x + x * x)) = 10 (49 + 7x + (7x + x2)) = 10 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) = 10 Solving 49 + 14x + x2 = 10 Solving for variable 'x'. Reorder the terms: 49 + -10 + 14x + x2 = 10 + -10 Combine like terms: 49 + -10 = 39 39 + 14x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 39 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 14x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 14x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 14x + x2 = 0 + -39 14x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 14x + x2 = -39 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 = -39 + 49 Reorder the terms: 49 + 14x + x2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + 14x + x2 = 10 Factor a perfect square on the left side: (x + 7)(x + 7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 7) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 7 = 3.16227766 Simplifying x + 7 = 3.16227766 Reorder the terms: 7 + x = 3.16227766 Solving 7 + x = 3.16227766 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 = 3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.16227766 + -7 x = 3.16227766 + -7 Combine like terms: 3.16227766 + -7 = -3.83772234 x = -3.83772234 Simplifying x = -3.83772234Subproblem 2
x + 7 = -3.16227766 Simplifying x + 7 = -3.16227766 Reorder the terms: 7 + x = -3.16227766 Solving 7 + x = -3.16227766 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 = -3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.16227766 + -7 x = -3.16227766 + -7 Combine like terms: -3.16227766 + -7 = -10.16227766 x = -10.16227766 Simplifying x = -10.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.83772234, -10.16227766}
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