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Simplifying (6 + -1x)(4 + -1x) = 30 Multiply (6 + -1x) * (4 + -1x) (6(4 + -1x) + -1x * (4 + -1x)) = 30 ((4 * 6 + -1x * 6) + -1x * (4 + -1x)) = 30 ((24 + -6x) + -1x * (4 + -1x)) = 30 (24 + -6x + (4 * -1x + -1x * -1x)) = 30 (24 + -6x + (-4x + 1x2)) = 30 Combine like terms: -6x + -4x = -10x (24 + -10x + 1x2) = 30 Solving 24 + -10x + 1x2 = 30 Solving for variable 'x'. Reorder the terms: 24 + -30 + -10x + 1x2 = 30 + -30 Combine like terms: 24 + -30 = -6 -6 + -10x + 1x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -6 + -10x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -10x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -10x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -10x + x2 = 0 + 6 -10x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -10x + x2 = 6 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 6 + 25 Reorder the terms: 25 + -10x + x2 = 6 + 25 Combine like terms: 6 + 25 = 31 25 + -10x + x2 = 31 Factor a perfect square on the left side: (x + -5)(x + -5) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -5) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -5 = 5.567764363 Simplifying x + -5 = 5.567764363 Reorder the terms: -5 + x = 5.567764363 Solving -5 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.567764363 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.567764363 + 5 x = 5.567764363 + 5 Combine like terms: 5.567764363 + 5 = 10.567764363 x = 10.567764363 Simplifying x = 10.567764363Subproblem 2
x + -5 = -5.567764363 Simplifying x + -5 = -5.567764363 Reorder the terms: -5 + x = -5.567764363 Solving -5 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.567764363 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.567764363 + 5 x = -5.567764363 + 5 Combine like terms: -5.567764363 + 5 = -0.567764363 x = -0.567764363 Simplifying x = -0.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.567764363, -0.567764363}
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