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Simplifying -1x2 + 9x + 49 = 0 Reorder the terms: 49 + 9x + -1x2 = 0 Solving 49 + 9x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + -9x + x2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -9x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -9x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -9x + x2 = 0 + 49 -9x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -9x + x2 = 49 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 = 49 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 49 + 20.25 Combine like terms: 49 + 20.25 = 69.25 20.25 + -9x + x2 = 69.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -4.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -4.5 = 8.321658489 Simplifying x + -4.5 = 8.321658489 Reorder the terms: -4.5 + x = 8.321658489 Solving -4.5 + x = 8.321658489 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 = 8.321658489 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 8.321658489 + 4.5 x = 8.321658489 + 4.5 Combine like terms: 8.321658489 + 4.5 = 12.821658489 x = 12.821658489 Simplifying x = 12.821658489Subproblem 2
x + -4.5 = -8.321658489 Simplifying x + -4.5 = -8.321658489 Reorder the terms: -4.5 + x = -8.321658489 Solving -4.5 + x = -8.321658489 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 = -8.321658489 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -8.321658489 + 4.5 x = -8.321658489 + 4.5 Combine like terms: -8.321658489 + 4.5 = -3.821658489 x = -3.821658489 Simplifying x = -3.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.821658489, -3.821658489}
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