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Simplifying x2 + 10x + -16 = 9 Reorder the terms: -16 + 10x + x2 = 9 Solving -16 + 10x + x2 = 9 Solving for variable 'x'. Reorder the terms: -16 + -9 + 10x + x2 = 9 + -9 Combine like terms: -16 + -9 = -25 -25 + 10x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -25 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 10x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 10x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 10x + x2 = 0 + 25 10x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 10x + x2 = 25 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 = 25 + 25 Reorder the terms: 25 + 10x + x2 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + 10x + x2 = 50 Factor a perfect square on the left side: (x + 5)(x + 5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 5) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 5 = 7.071067812 Simplifying x + 5 = 7.071067812 Reorder the terms: 5 + x = 7.071067812 Solving 5 + x = 7.071067812 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 = 7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.071067812 + -5 x = 7.071067812 + -5 Combine like terms: 7.071067812 + -5 = 2.071067812 x = 2.071067812 Simplifying x = 2.071067812Subproblem 2
x + 5 = -7.071067812 Simplifying x + 5 = -7.071067812 Reorder the terms: 5 + x = -7.071067812 Solving 5 + x = -7.071067812 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 = -7.071067812 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.071067812 + -5 x = -7.071067812 + -5 Combine like terms: -7.071067812 + -5 = -12.071067812 x = -12.071067812 Simplifying x = -12.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.071067812, -12.071067812}
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