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Simplifying x2 + 6x + 3 = 78 Reorder the terms: 3 + 6x + x2 = 78 Solving 3 + 6x + x2 = 78 Solving for variable 'x'. Reorder the terms: 3 + -78 + 6x + x2 = 78 + -78 Combine like terms: 3 + -78 = -75 -75 + 6x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -75 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 6x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 6x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 6x + x2 = 0 + 75 6x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 6x + x2 = 75 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 = 75 + 9 Reorder the terms: 9 + 6x + x2 = 75 + 9 Combine like terms: 75 + 9 = 84 9 + 6x + x2 = 84 Factor a perfect square on the left side: (x + 3)(x + 3) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 3) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 3 = 9.16515139 Simplifying x + 3 = 9.16515139 Reorder the terms: 3 + x = 9.16515139 Solving 3 + x = 9.16515139 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 = 9.16515139 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.16515139 + -3 x = 9.16515139 + -3 Combine like terms: 9.16515139 + -3 = 6.16515139 x = 6.16515139 Simplifying x = 6.16515139Subproblem 2
x + 3 = -9.16515139 Simplifying x + 3 = -9.16515139 Reorder the terms: 3 + x = -9.16515139 Solving 3 + x = -9.16515139 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 = -9.16515139 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.16515139 + -3 x = -9.16515139 + -3 Combine like terms: -9.16515139 + -3 = -12.16515139 x = -12.16515139 Simplifying x = -12.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.16515139, -12.16515139}
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