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Simplifying x2 + -9x + -763 = 0 Reorder the terms: -763 + -9x + x2 = 0 Solving -763 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '763' to each side of the equation. -763 + -9x + 763 + x2 = 0 + 763 Reorder the terms: -763 + 763 + -9x + x2 = 0 + 763 Combine like terms: -763 + 763 = 0 0 + -9x + x2 = 0 + 763 -9x + x2 = 0 + 763 Combine like terms: 0 + 763 = 763 -9x + x2 = 763 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 = 763 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 763 + 20.25 Combine like terms: 763 + 20.25 = 783.25 20.25 + -9x + x2 = 783.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 783.25 Calculate the square root of the right side: 27.986603938 Break this problem into two subproblems by setting (x + -4.5) equal to 27.986603938 and -27.986603938.Subproblem 1
x + -4.5 = 27.986603938 Simplifying x + -4.5 = 27.986603938 Reorder the terms: -4.5 + x = 27.986603938 Solving -4.5 + x = 27.986603938 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 = 27.986603938 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 27.986603938 + 4.5 x = 27.986603938 + 4.5 Combine like terms: 27.986603938 + 4.5 = 32.486603938 x = 32.486603938 Simplifying x = 32.486603938Subproblem 2
x + -4.5 = -27.986603938 Simplifying x + -4.5 = -27.986603938 Reorder the terms: -4.5 + x = -27.986603938 Solving -4.5 + x = -27.986603938 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 = -27.986603938 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -27.986603938 + 4.5 x = -27.986603938 + 4.5 Combine like terms: -27.986603938 + 4.5 = -23.486603938 x = -23.486603938 Simplifying x = -23.486603938Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.486603938, -23.486603938}
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