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Simplifying x = x2 + 8x + 7 Reorder the terms: x = 7 + 8x + x2 Solving x = 7 + 8x + x2 Solving for variable 'x'. Reorder the terms: -7 + x + -8x + -1x2 = 7 + 8x + x2 + -7 + -8x + -1x2 Combine like terms: x + -8x = -7x -7 + -7x + -1x2 = 7 + 8x + x2 + -7 + -8x + -1x2 Reorder the terms: -7 + -7x + -1x2 = 7 + -7 + 8x + -8x + x2 + -1x2 Combine like terms: 7 + -7 = 0 -7 + -7x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -7 + -7x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -7 + -7x + -1x2 = 0 + x2 + -1x2 -7 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -7 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 7x + x2)' equal to zero and attempt to solve: Simplifying 7 + 7x + x2 = 0 Solving 7 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 7x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7x + x2 = 0 + -7 7x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 7x + x2 = -7 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -7 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + 7x + x2 = 5.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 3.5 = 2.291287847 Simplifying x + 3.5 = 2.291287847 Reorder the terms: 3.5 + x = 2.291287847 Solving 3.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.291287847 + -3.5 x = 2.291287847 + -3.5 Combine like terms: 2.291287847 + -3.5 = -1.208712153 x = -1.208712153 Simplifying x = -1.208712153Subproblem 2
x + 3.5 = -2.291287847 Simplifying x + 3.5 = -2.291287847 Reorder the terms: 3.5 + x = -2.291287847 Solving 3.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.291287847 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.291287847 + -3.5 x = -2.291287847 + -3.5 Combine like terms: -2.291287847 + -3.5 = -5.791287847 x = -5.791287847 Simplifying x = -5.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.208712153, -5.791287847}Solution
x = {-1.208712153, -5.791287847}
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