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Simplifying 5x + 60 = 4x2 + -12x Reorder the terms: 60 + 5x = 4x2 + -12x Reorder the terms: 60 + 5x = -12x + 4x2 Solving 60 + 5x = -12x + 4x2 Solving for variable 'x'. Combine like terms: 5x + 12x = 17x 60 + 17x + -4x2 = -12x + 4x2 + 12x + -4x2 Reorder the terms: 60 + 17x + -4x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 60 + 17x + -4x2 = 0 + 4x2 + -4x2 60 + 17x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 60 + 17x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15 + -4.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -4.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -4.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4.25x + x2 = 0 + 15 -4.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4.25x + x2 = 15 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 15 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 15 + 4.515625 Combine like terms: 15 + 4.515625 = 19.515625 4.515625 + -4.25x + x2 = 19.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 19.515625 Calculate the square root of the right side: 4.417649262 Break this problem into two subproblems by setting (x + -2.125) equal to 4.417649262 and -4.417649262.Subproblem 1
x + -2.125 = 4.417649262 Simplifying x + -2.125 = 4.417649262 Reorder the terms: -2.125 + x = 4.417649262 Solving -2.125 + x = 4.417649262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 4.417649262 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 4.417649262 + 2.125 x = 4.417649262 + 2.125 Combine like terms: 4.417649262 + 2.125 = 6.542649262 x = 6.542649262 Simplifying x = 6.542649262Subproblem 2
x + -2.125 = -4.417649262 Simplifying x + -2.125 = -4.417649262 Reorder the terms: -2.125 + x = -4.417649262 Solving -2.125 + x = -4.417649262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -4.417649262 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -4.417649262 + 2.125 x = -4.417649262 + 2.125 Combine like terms: -4.417649262 + 2.125 = -2.292649262 x = -2.292649262 Simplifying x = -2.292649262Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.542649262, -2.292649262}
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