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Simplifying (x + 10)(x + -3) = 25 Reorder the terms: (10 + x)(x + -3) = 25 Reorder the terms: (10 + x)(-3 + x) = 25 Multiply (10 + x) * (-3 + x) (10(-3 + x) + x(-3 + x)) = 25 ((-3 * 10 + x * 10) + x(-3 + x)) = 25 ((-30 + 10x) + x(-3 + x)) = 25 (-30 + 10x + (-3 * x + x * x)) = 25 (-30 + 10x + (-3x + x2)) = 25 Combine like terms: 10x + -3x = 7x (-30 + 7x + x2) = 25 Solving -30 + 7x + x2 = 25 Solving for variable 'x'. Reorder the terms: -30 + -25 + 7x + x2 = 25 + -25 Combine like terms: -30 + -25 = -55 -55 + 7x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -55 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 7x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 7x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 7x + x2 = 0 + 55 7x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 7x + x2 = 55 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 55 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 55 + 12.25 Combine like terms: 55 + 12.25 = 67.25 12.25 + 7x + x2 = 67.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + 3.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + 3.5 = 8.200609733 Simplifying x + 3.5 = 8.200609733 Reorder the terms: 3.5 + x = 8.200609733 Solving 3.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 8.200609733 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.200609733 + -3.5 x = 8.200609733 + -3.5 Combine like terms: 8.200609733 + -3.5 = 4.700609733 x = 4.700609733 Simplifying x = 4.700609733Subproblem 2
x + 3.5 = -8.200609733 Simplifying x + 3.5 = -8.200609733 Reorder the terms: 3.5 + x = -8.200609733 Solving 3.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -8.200609733 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.200609733 + -3.5 x = -8.200609733 + -3.5 Combine like terms: -8.200609733 + -3.5 = -11.700609733 x = -11.700609733 Simplifying x = -11.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.700609733, -11.700609733}
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