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Simplifying 4x(x + -12) = 55 Reorder the terms: 4x(-12 + x) = 55 (-12 * 4x + x * 4x) = 55 (-48x + 4x2) = 55 Solving -48x + 4x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + -48x + 4x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -48x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -13.75 + -12x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + -12x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + -12x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + -12x + x2 = 0 + 13.75 -12x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 -12x + x2 = 13.75 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 = 13.75 + 36 Reorder the terms: 36 + -12x + x2 = 13.75 + 36 Combine like terms: 13.75 + 36 = 49.75 36 + -12x + x2 = 49.75 Factor a perfect square on the left side: (x + -6)(x + -6) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (x + -6) equal to 7.05336799 and -7.05336799.Subproblem 1
x + -6 = 7.05336799 Simplifying x + -6 = 7.05336799 Reorder the terms: -6 + x = 7.05336799 Solving -6 + x = 7.05336799 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 = 7.05336799 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.05336799 + 6 x = 7.05336799 + 6 Combine like terms: 7.05336799 + 6 = 13.05336799 x = 13.05336799 Simplifying x = 13.05336799Subproblem 2
x + -6 = -7.05336799 Simplifying x + -6 = -7.05336799 Reorder the terms: -6 + x = -7.05336799 Solving -6 + x = -7.05336799 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 = -7.05336799 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.05336799 + 6 x = -7.05336799 + 6 Combine like terms: -7.05336799 + 6 = -1.05336799 x = -1.05336799 Simplifying x = -1.05336799Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.05336799, -1.05336799}
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