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Simplifying x2 + -4x + -84 = 0 Reorder the terms: -84 + -4x + x2 = 0 Solving -84 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -4x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + -4x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -4x + x2 = 0 + 84 -4x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 -4x + x2 = 84 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 84 + 4 Reorder the terms: 4 + -4x + x2 = 84 + 4 Combine like terms: 84 + 4 = 88 4 + -4x + x2 = 88 Factor a perfect square on the left side: (x + -2)(x + -2) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -2) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -2 = 9.38083152 Simplifying x + -2 = 9.38083152 Reorder the terms: -2 + x = 9.38083152 Solving -2 + x = 9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.38083152 + 2 x = 9.38083152 + 2 Combine like terms: 9.38083152 + 2 = 11.38083152 x = 11.38083152 Simplifying x = 11.38083152Subproblem 2
x + -2 = -9.38083152 Simplifying x + -2 = -9.38083152 Reorder the terms: -2 + x = -9.38083152 Solving -2 + x = -9.38083152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.38083152 + 2 x = -9.38083152 + 2 Combine like terms: -9.38083152 + 2 = -7.38083152 x = -7.38083152 Simplifying x = -7.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.38083152, -7.38083152}
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