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Simplifying (x + -7)(x + -7) = 28 Reorder the terms: (-7 + x)(x + -7) = 28 Reorder the terms: (-7 + x)(-7 + x) = 28 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 28 ((-7 * -7 + x * -7) + x(-7 + x)) = 28 ((49 + -7x) + x(-7 + x)) = 28 (49 + -7x + (-7 * x + x * x)) = 28 (49 + -7x + (-7x + x2)) = 28 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 28 Solving 49 + -14x + x2 = 28 Solving for variable 'x'. Reorder the terms: 49 + -28 + -14x + x2 = 28 + -28 Combine like terms: 49 + -28 = 21 21 + -14x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 21 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -14x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -14x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -14x + x2 = 0 + -21 -14x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -14x + x2 = -21 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 = -21 + 49 Reorder the terms: 49 + -14x + x2 = -21 + 49 Combine like terms: -21 + 49 = 28 49 + -14x + x2 = 28 Factor a perfect square on the left side: (x + -7)(x + -7) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -7) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -7 = 5.291502622 Simplifying x + -7 = 5.291502622 Reorder the terms: -7 + x = 5.291502622 Solving -7 + x = 5.291502622 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 = 5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.291502622 + 7 x = 5.291502622 + 7 Combine like terms: 5.291502622 + 7 = 12.291502622 x = 12.291502622 Simplifying x = 12.291502622Subproblem 2
x + -7 = -5.291502622 Simplifying x + -7 = -5.291502622 Reorder the terms: -7 + x = -5.291502622 Solving -7 + x = -5.291502622 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 = -5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.291502622 + 7 x = -5.291502622 + 7 Combine like terms: -5.291502622 + 7 = 1.708497378 x = 1.708497378 Simplifying x = 1.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.291502622, 1.708497378}
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