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Simplifying (x + -4)(x + 3) = 20 Reorder the terms: (-4 + x)(x + 3) = 20 Reorder the terms: (-4 + x)(3 + x) = 20 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) = 20 ((3 * -4 + x * -4) + x(3 + x)) = 20 ((-12 + -4x) + x(3 + x)) = 20 (-12 + -4x + (3 * x + x * x)) = 20 (-12 + -4x + (3x + x2)) = 20 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) = 20 Solving -12 + -1x + x2 = 20 Solving for variable 'x'. Reorder the terms: -12 + -20 + -1x + x2 = 20 + -20 Combine like terms: -12 + -20 = -32 -32 + -1x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -32 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -1x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -1x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1x + x2 = 0 + 32 -1x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -1x + x2 = 32 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 = 32 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 32 + 0.25 Combine like terms: 32 + 0.25 = 32.25 0.25 + -1x + x2 = 32.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -0.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -0.5 = 5.678908346 Simplifying x + -0.5 = 5.678908346 Reorder the terms: -0.5 + x = 5.678908346 Solving -0.5 + x = 5.678908346 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 = 5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.678908346 + 0.5 x = 5.678908346 + 0.5 Combine like terms: 5.678908346 + 0.5 = 6.178908346 x = 6.178908346 Simplifying x = 6.178908346Subproblem 2
x + -0.5 = -5.678908346 Simplifying x + -0.5 = -5.678908346 Reorder the terms: -0.5 + x = -5.678908346 Solving -0.5 + x = -5.678908346 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 = -5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.678908346 + 0.5 x = -5.678908346 + 0.5 Combine like terms: -5.678908346 + 0.5 = -5.178908346 x = -5.178908346 Simplifying x = -5.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.178908346, -5.178908346}
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