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Simplifying 4.5 = x2 + 12x Reorder the terms: 4.5 = 12x + x2 Solving 4.5 = 12x + x2 Solving for variable 'x'. Reorder the terms: 4.5 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 4.5 + -12x + -1x2 = 0 + x2 + -1x2 4.5 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4.5 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4.5 + 12x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 12x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 12x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 12x + x2 = 0 + 4.5 12x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 12x + x2 = 4.5 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 4.5 + 36 Reorder the terms: 36 + 12x + x2 = 4.5 + 36 Combine like terms: 4.5 + 36 = 40.5 36 + 12x + x2 = 40.5 Factor a perfect square on the left side: (x + 6)(x + 6) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (x + 6) equal to 6.363961031 and -6.363961031.Subproblem 1
x + 6 = 6.363961031 Simplifying x + 6 = 6.363961031 Reorder the terms: 6 + x = 6.363961031 Solving 6 + x = 6.363961031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.363961031 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.363961031 + -6 x = 6.363961031 + -6 Combine like terms: 6.363961031 + -6 = 0.363961031 x = 0.363961031 Simplifying x = 0.363961031Subproblem 2
x + 6 = -6.363961031 Simplifying x + 6 = -6.363961031 Reorder the terms: 6 + x = -6.363961031 Solving 6 + x = -6.363961031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.363961031 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.363961031 + -6 x = -6.363961031 + -6 Combine like terms: -6.363961031 + -6 = -12.363961031 x = -12.363961031 Simplifying x = -12.363961031Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.363961031, -12.363961031}
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