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Simplifying x2 + 8x + -5 = 10 Reorder the terms: -5 + 8x + x2 = 10 Solving -5 + 8x + x2 = 10 Solving for variable 'x'. Reorder the terms: -5 + -10 + 8x + x2 = 10 + -10 Combine like terms: -5 + -10 = -15 -15 + 8x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -15 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 8x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 8x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 8x + x2 = 0 + 15 8x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 8x + x2 = 15 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 15 + 16 Reorder the terms: 16 + 8x + x2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + 8x + x2 = 31 Factor a perfect square on the left side: (x + 4)(x + 4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 4) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 4 = 5.567764363 Simplifying x + 4 = 5.567764363 Reorder the terms: 4 + x = 5.567764363 Solving 4 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.567764363 + -4 x = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 x = 1.567764363 Simplifying x = 1.567764363Subproblem 2
x + 4 = -5.567764363 Simplifying x + 4 = -5.567764363 Reorder the terms: 4 + x = -5.567764363 Solving 4 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.567764363 + -4 x = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 x = -9.567764363 Simplifying x = -9.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.567764363, -9.567764363}
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