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Simplifying x2 + 8 = 10x + -4 Reorder the terms: 8 + x2 = 10x + -4 Reorder the terms: 8 + x2 = -4 + 10x Solving 8 + x2 = -4 + 10x Solving for variable 'x'. Reorder the terms: 8 + 4 + -10x + x2 = -4 + 10x + 4 + -10x Combine like terms: 8 + 4 = 12 12 + -10x + x2 = -4 + 10x + 4 + -10x Reorder the terms: 12 + -10x + x2 = -4 + 4 + 10x + -10x Combine like terms: -4 + 4 = 0 12 + -10x + x2 = 0 + 10x + -10x 12 + -10x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 12 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -10x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -10x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -10x + x2 = 0 + -12 -10x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -10x + x2 = -12 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 = -12 + 25 Reorder the terms: 25 + -10x + x2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + -10x + x2 = 13 Factor a perfect square on the left side: (x + -5)(x + -5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -5) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -5 = 3.605551275 Simplifying x + -5 = 3.605551275 Reorder the terms: -5 + x = 3.605551275 Solving -5 + x = 3.605551275 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 = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.605551275 + 5 x = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 x = 8.605551275 Simplifying x = 8.605551275Subproblem 2
x + -5 = -3.605551275 Simplifying x + -5 = -3.605551275 Reorder the terms: -5 + x = -3.605551275 Solving -5 + x = -3.605551275 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 = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.605551275 + 5 x = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 x = 1.394448725 Simplifying x = 1.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.605551275, 1.394448725}
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