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Simplifying (x + -7)(x + -7) = 24 Reorder the terms: (-7 + x)(x + -7) = 24 Reorder the terms: (-7 + x)(-7 + x) = 24 Multiply (-7 + x) * (-7 + x) (-7(-7 + x) + x(-7 + x)) = 24 ((-7 * -7 + x * -7) + x(-7 + x)) = 24 ((49 + -7x) + x(-7 + x)) = 24 (49 + -7x + (-7 * x + x * x)) = 24 (49 + -7x + (-7x + x2)) = 24 Combine like terms: -7x + -7x = -14x (49 + -14x + x2) = 24 Solving 49 + -14x + x2 = 24 Solving for variable 'x'. Reorder the terms: 49 + -24 + -14x + x2 = 24 + -24 Combine like terms: 49 + -24 = 25 25 + -14x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 25 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -14x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -14x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -14x + x2 = 0 + -25 -14x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -14x + x2 = -25 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 = -25 + 49 Reorder the terms: 49 + -14x + x2 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + -14x + x2 = 24 Factor a perfect square on the left side: (x + -7)(x + -7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -7) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -7 = 4.898979486 Simplifying x + -7 = 4.898979486 Reorder the terms: -7 + x = 4.898979486 Solving -7 + x = 4.898979486 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 = 4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.898979486 + 7 x = 4.898979486 + 7 Combine like terms: 4.898979486 + 7 = 11.898979486 x = 11.898979486 Simplifying x = 11.898979486Subproblem 2
x + -7 = -4.898979486 Simplifying x + -7 = -4.898979486 Reorder the terms: -7 + x = -4.898979486 Solving -7 + x = -4.898979486 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 = -4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.898979486 + 7 x = -4.898979486 + 7 Combine like terms: -4.898979486 + 7 = 2.101020514 x = 2.101020514 Simplifying x = 2.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.898979486, 2.101020514}
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