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Simplifying 14.5625 = (x + -2.75)(x + -2.75) Reorder the terms: 14.5625 = (-2.75 + x)(x + -2.75) Reorder the terms: 14.5625 = (-2.75 + x)(-2.75 + x) Multiply (-2.75 + x) * (-2.75 + x) 14.5625 = (-2.75(-2.75 + x) + x(-2.75 + x)) 14.5625 = ((-2.75 * -2.75 + x * -2.75) + x(-2.75 + x)) 14.5625 = ((7.5625 + -2.75x) + x(-2.75 + x)) 14.5625 = (7.5625 + -2.75x + (-2.75 * x + x * x)) 14.5625 = (7.5625 + -2.75x + (-2.75x + x2)) Combine like terms: -2.75x + -2.75x = -5.5x 14.5625 = (7.5625 + -5.5x + x2) Solving 14.5625 = 7.5625 + -5.5x + x2 Solving for variable 'x'. Combine like terms: 14.5625 + -7.5625 = 7 7 + 5.5x + -1x2 = 7.5625 + -5.5x + x2 + -7.5625 + 5.5x + -1x2 Reorder the terms: 7 + 5.5x + -1x2 = 7.5625 + -7.5625 + -5.5x + 5.5x + x2 + -1x2 Combine like terms: 7.5625 + -7.5625 = 0.0000 7 + 5.5x + -1x2 = 0.0000 + -5.5x + 5.5x + x2 + -1x2 7 + 5.5x + -1x2 = -5.5x + 5.5x + x2 + -1x2 Combine like terms: -5.5x + 5.5x = 0.0 7 + 5.5x + -1x2 = 0.0 + x2 + -1x2 7 + 5.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 5.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + -5.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.5x + x2 = 0 + 7 -5.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.5x + x2 = 7 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 7 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 7 + 7.5625 Combine like terms: 7 + 7.5625 = 14.5625 7.5625 + -5.5x + x2 = 14.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 14.5625 Calculate the square root of the right side: 3.816084381 Break this problem into two subproblems by setting (x + -2.75) equal to 3.816084381 and -3.816084381.Subproblem 1
x + -2.75 = 3.816084381 Simplifying x + -2.75 = 3.816084381 Reorder the terms: -2.75 + x = 3.816084381 Solving -2.75 + x = 3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.816084381 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.816084381 + 2.75 x = 3.816084381 + 2.75 Combine like terms: 3.816084381 + 2.75 = 6.566084381 x = 6.566084381 Simplifying x = 6.566084381Subproblem 2
x + -2.75 = -3.816084381 Simplifying x + -2.75 = -3.816084381 Reorder the terms: -2.75 + x = -3.816084381 Solving -2.75 + x = -3.816084381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.816084381 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.816084381 + 2.75 x = -3.816084381 + 2.75 Combine like terms: -3.816084381 + 2.75 = -1.066084381 x = -1.066084381 Simplifying x = -1.066084381Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.566084381, -1.066084381}
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