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Simplifying x = -1x2 + -8x + -15 Reorder the terms: x = -15 + -8x + -1x2 Solving x = -15 + -8x + -1x2 Solving for variable 'x'. Reorder the terms: 15 + x + 8x + x2 = -15 + -8x + -1x2 + 15 + 8x + x2 Combine like terms: x + 8x = 9x 15 + 9x + x2 = -15 + -8x + -1x2 + 15 + 8x + x2 Reorder the terms: 15 + 9x + x2 = -15 + 15 + -8x + 8x + -1x2 + x2 Combine like terms: -15 + 15 = 0 15 + 9x + x2 = 0 + -8x + 8x + -1x2 + x2 15 + 9x + x2 = -8x + 8x + -1x2 + x2 Combine like terms: -8x + 8x = 0 15 + 9x + x2 = 0 + -1x2 + x2 15 + 9x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 15 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 9x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 9x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 9x + x2 = 0 + -15 9x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 9x + x2 = -15 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 = -15 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + 9x + x2 = 5.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 4.5 = 2.291287847 Simplifying x + 4.5 = 2.291287847 Reorder the terms: 4.5 + x = 2.291287847 Solving 4.5 + x = 2.291287847 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 = 2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.291287847 + -4.5 x = 2.291287847 + -4.5 Combine like terms: 2.291287847 + -4.5 = -2.208712153 x = -2.208712153 Simplifying x = -2.208712153Subproblem 2
x + 4.5 = -2.291287847 Simplifying x + 4.5 = -2.291287847 Reorder the terms: 4.5 + x = -2.291287847 Solving 4.5 + x = -2.291287847 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 = -2.291287847 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.291287847 + -4.5 x = -2.291287847 + -4.5 Combine like terms: -2.291287847 + -4.5 = -6.791287847 x = -6.791287847 Simplifying x = -6.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.208712153, -6.791287847}
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