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Simplifying (x + -7)(x + 7) = 2x Reorder the terms: (-7 + x)(x + 7) = 2x Reorder the terms: (-7 + x)(7 + x) = 2x Multiply (-7 + x) * (7 + x) (-7(7 + x) + x(7 + x)) = 2x ((7 * -7 + x * -7) + x(7 + x)) = 2x ((-49 + -7x) + x(7 + x)) = 2x (-49 + -7x + (7 * x + x * x)) = 2x (-49 + -7x + (7x + x2)) = 2x Combine like terms: -7x + 7x = 0 (-49 + 0 + x2) = 2x (-49 + x2) = 2x Solving -49 + x2 = 2x Solving for variable 'x'. Reorder the terms: -49 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -49 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -2x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -2x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -2x + x2 = 0 + 49 -2x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -2x + x2 = 49 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 49 + 1 Reorder the terms: 1 + -2x + x2 = 49 + 1 Combine like terms: 49 + 1 = 50 1 + -2x + x2 = 50 Factor a perfect square on the left side: (x + -1)(x + -1) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -1) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -1 = 7.071067812 Simplifying x + -1 = 7.071067812 Reorder the terms: -1 + x = 7.071067812 Solving -1 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.071067812 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.071067812 + 1 x = 7.071067812 + 1 Combine like terms: 7.071067812 + 1 = 8.071067812 x = 8.071067812 Simplifying x = 8.071067812Subproblem 2
x + -1 = -7.071067812 Simplifying x + -1 = -7.071067812 Reorder the terms: -1 + x = -7.071067812 Solving -1 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.071067812 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.071067812 + 1 x = -7.071067812 + 1 Combine like terms: -7.071067812 + 1 = -6.071067812 x = -6.071067812 Simplifying x = -6.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.071067812, -6.071067812}
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