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Simplifying x2 + -7x + -75 = 0 Reorder the terms: -75 + -7x + x2 = 0 Solving -75 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -7x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -7x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -7x + x2 = 0 + 75 -7x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -7x + x2 = 75 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 = 75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 75 + 12.25 Combine like terms: 75 + 12.25 = 87.25 12.25 + -7x + x2 = 87.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 87.25 Calculate the square root of the right side: 9.340770846 Break this problem into two subproblems by setting (x + -3.5) equal to 9.340770846 and -9.340770846.Subproblem 1
x + -3.5 = 9.340770846 Simplifying x + -3.5 = 9.340770846 Reorder the terms: -3.5 + x = 9.340770846 Solving -3.5 + x = 9.340770846 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 = 9.340770846 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 9.340770846 + 3.5 x = 9.340770846 + 3.5 Combine like terms: 9.340770846 + 3.5 = 12.840770846 x = 12.840770846 Simplifying x = 12.840770846Subproblem 2
x + -3.5 = -9.340770846 Simplifying x + -3.5 = -9.340770846 Reorder the terms: -3.5 + x = -9.340770846 Solving -3.5 + x = -9.340770846 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 = -9.340770846 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -9.340770846 + 3.5 x = -9.340770846 + 3.5 Combine like terms: -9.340770846 + 3.5 = -5.840770846 x = -5.840770846 Simplifying x = -5.840770846Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.840770846, -5.840770846}
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