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Simplifying 6x2 + 21x + -12 = 112 Reorder the terms: -12 + 21x + 6x2 = 112 Solving -12 + 21x + 6x2 = 112 Solving for variable 'x'. Reorder the terms: -12 + -112 + 21x + 6x2 = 112 + -112 Combine like terms: -12 + -112 = -124 -124 + 21x + 6x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -124 + 21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -20.66666667 + 3.5x + x2 = 0 Move the constant term to the right: Add '20.66666667' to each side of the equation. -20.66666667 + 3.5x + 20.66666667 + x2 = 0 + 20.66666667 Reorder the terms: -20.66666667 + 20.66666667 + 3.5x + x2 = 0 + 20.66666667 Combine like terms: -20.66666667 + 20.66666667 = 0.00000000 0.00000000 + 3.5x + x2 = 0 + 20.66666667 3.5x + x2 = 0 + 20.66666667 Combine like terms: 0 + 20.66666667 = 20.66666667 3.5x + x2 = 20.66666667 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 20.66666667 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 20.66666667 + 3.0625 Combine like terms: 20.66666667 + 3.0625 = 23.72916667 3.0625 + 3.5x + x2 = 23.72916667 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 23.72916667 Calculate the square root of the right side: 4.871259249 Break this problem into two subproblems by setting (x + 1.75) equal to 4.871259249 and -4.871259249.Subproblem 1
x + 1.75 = 4.871259249 Simplifying x + 1.75 = 4.871259249 Reorder the terms: 1.75 + x = 4.871259249 Solving 1.75 + x = 4.871259249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 4.871259249 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 4.871259249 + -1.75 x = 4.871259249 + -1.75 Combine like terms: 4.871259249 + -1.75 = 3.121259249 x = 3.121259249 Simplifying x = 3.121259249Subproblem 2
x + 1.75 = -4.871259249 Simplifying x + 1.75 = -4.871259249 Reorder the terms: 1.75 + x = -4.871259249 Solving 1.75 + x = -4.871259249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -4.871259249 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -4.871259249 + -1.75 x = -4.871259249 + -1.75 Combine like terms: -4.871259249 + -1.75 = -6.621259249 x = -6.621259249 Simplifying x = -6.621259249Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.121259249, -6.621259249}
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