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Simplifying x2 + -6x + -76 = 3 Reorder the terms: -76 + -6x + x2 = 3 Solving -76 + -6x + x2 = 3 Solving for variable 'x'. Reorder the terms: -76 + -3 + -6x + x2 = 3 + -3 Combine like terms: -76 + -3 = -79 -79 + -6x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -79 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -6x + 79 + x2 = 0 + 79 Reorder the terms: -79 + 79 + -6x + x2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -6x + x2 = 0 + 79 -6x + x2 = 0 + 79 Combine like terms: 0 + 79 = 79 -6x + x2 = 79 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 79 + 9 Reorder the terms: 9 + -6x + x2 = 79 + 9 Combine like terms: 79 + 9 = 88 9 + -6x + x2 = 88 Factor a perfect square on the left side: (x + -3)(x + -3) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -3) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -3 = 9.38083152 Simplifying x + -3 = 9.38083152 Reorder the terms: -3 + x = 9.38083152 Solving -3 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.38083152 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.38083152 + 3 x = 9.38083152 + 3 Combine like terms: 9.38083152 + 3 = 12.38083152 x = 12.38083152 Simplifying x = 12.38083152Subproblem 2
x + -3 = -9.38083152 Simplifying x + -3 = -9.38083152 Reorder the terms: -3 + x = -9.38083152 Solving -3 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.38083152 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.38083152 + 3 x = -9.38083152 + 3 Combine like terms: -9.38083152 + 3 = -6.38083152 x = -6.38083152 Simplifying x = -6.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.38083152, -6.38083152}
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