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Simplifying (x + 7)(x + 7) = 13 Reorder the terms: (7 + x)(x + 7) = 13 Reorder the terms: (7 + x)(7 + x) = 13 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) = 13 ((7 * 7 + x * 7) + x(7 + x)) = 13 ((49 + 7x) + x(7 + x)) = 13 (49 + 7x + (7 * x + x * x)) = 13 (49 + 7x + (7x + x2)) = 13 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) = 13 Solving 49 + 14x + x2 = 13 Solving for variable 'x'. Reorder the terms: 49 + -13 + 14x + x2 = 13 + -13 Combine like terms: 49 + -13 = 36 36 + 14x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 36 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 14x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 14x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 14x + x2 = 0 + -36 14x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 14x + x2 = -36 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 = -36 + 49 Reorder the terms: 49 + 14x + x2 = -36 + 49 Combine like terms: -36 + 49 = 13 49 + 14x + x2 = 13 Factor a perfect square on the left side: (x + 7)(x + 7) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 7) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 7 = 3.605551275 Simplifying x + 7 = 3.605551275 Reorder the terms: 7 + x = 3.605551275 Solving 7 + x = 3.605551275 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 = 3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.605551275 + -7 x = 3.605551275 + -7 Combine like terms: 3.605551275 + -7 = -3.394448725 x = -3.394448725 Simplifying x = -3.394448725Subproblem 2
x + 7 = -3.605551275 Simplifying x + 7 = -3.605551275 Reorder the terms: 7 + x = -3.605551275 Solving 7 + x = -3.605551275 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 = -3.605551275 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.605551275 + -7 x = -3.605551275 + -7 Combine like terms: -3.605551275 + -7 = -10.605551275 x = -10.605551275 Simplifying x = -10.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.394448725, -10.605551275}
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