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Simplifying (x + -2)(x + -7) = 20 Reorder the terms: (-2 + x)(x + -7) = 20 Reorder the terms: (-2 + x)(-7 + x) = 20 Multiply (-2 + x) * (-7 + x) (-2(-7 + x) + x(-7 + x)) = 20 ((-7 * -2 + x * -2) + x(-7 + x)) = 20 ((14 + -2x) + x(-7 + x)) = 20 (14 + -2x + (-7 * x + x * x)) = 20 (14 + -2x + (-7x + x2)) = 20 Combine like terms: -2x + -7x = -9x (14 + -9x + x2) = 20 Solving 14 + -9x + x2 = 20 Solving for variable 'x'. Reorder the terms: 14 + -20 + -9x + x2 = 20 + -20 Combine like terms: 14 + -20 = -6 -6 + -9x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -6 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -9x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -9x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -9x + x2 = 0 + 6 -9x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -9x + x2 = 6 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 6 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 6 + 20.25 Combine like terms: 6 + 20.25 = 26.25 20.25 + -9x + x2 = 26.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -4.5 = 5.123475383 Simplifying x + -4.5 = 5.123475383 Reorder the terms: -4.5 + x = 5.123475383 Solving -4.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.123475383 + 4.5 x = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 x = 9.623475383 Simplifying x = 9.623475383Subproblem 2
x + -4.5 = -5.123475383 Simplifying x + -4.5 = -5.123475383 Reorder the terms: -4.5 + x = -5.123475383 Solving -4.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.123475383 + 4.5 x = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 x = -0.623475383 Simplifying x = -0.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.623475383, -0.623475383}
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