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Simplifying (x + 5)(x + -5) = x Reorder the terms: (5 + x)(x + -5) = x Reorder the terms: (5 + x)(-5 + x) = x Multiply (5 + x) * (-5 + x) (5(-5 + x) + x(-5 + x)) = x ((-5 * 5 + x * 5) + x(-5 + x)) = x ((-25 + 5x) + x(-5 + x)) = x (-25 + 5x + (-5 * x + x * x)) = x (-25 + 5x + (-5x + x2)) = x Combine like terms: 5x + -5x = 0 (-25 + 0 + x2) = x (-25 + x2) = x Solving -25 + x2 = x Solving for variable 'x'. Reorder the terms: -25 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -25 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -1x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -1x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x + x2 = 0 + 25 -1x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -1x + x2 = 25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 25 + 0.25 Combine like terms: 25 + 0.25 = 25.25 0.25 + -1x + x2 = 25.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (x + -0.5) equal to 5.024937811 and -5.024937811.Subproblem 1
x + -0.5 = 5.024937811 Simplifying x + -0.5 = 5.024937811 Reorder the terms: -0.5 + x = 5.024937811 Solving -0.5 + x = 5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.024937811 + 0.5 x = 5.024937811 + 0.5 Combine like terms: 5.024937811 + 0.5 = 5.524937811 x = 5.524937811 Simplifying x = 5.524937811Subproblem 2
x + -0.5 = -5.024937811 Simplifying x + -0.5 = -5.024937811 Reorder the terms: -0.5 + x = -5.024937811 Solving -0.5 + x = -5.024937811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.024937811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.024937811 + 0.5 x = -5.024937811 + 0.5 Combine like terms: -5.024937811 + 0.5 = -4.524937811 x = -4.524937811 Simplifying x = -4.524937811Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.524937811, -4.524937811}
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