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Simplifying 12x2 + -48x + 35 = 0 Reorder the terms: 35 + -48x + 12x2 = 0 Solving 35 + -48x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 2.916666667 + -4x + x2 = 0 Move the constant term to the right: Add '-2.916666667' to each side of the equation. 2.916666667 + -4x + -2.916666667 + x2 = 0 + -2.916666667 Reorder the terms: 2.916666667 + -2.916666667 + -4x + x2 = 0 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -2.916666667 -4x + x2 = 0 + -2.916666667 Combine like terms: 0 + -2.916666667 = -2.916666667 -4x + x2 = -2.916666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.916666667 + 4 Reorder the terms: 4 + -4x + x2 = -2.916666667 + 4 Combine like terms: -2.916666667 + 4 = 1.083333333 4 + -4x + x2 = 1.083333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.083333333 Calculate the square root of the right side: 1.040833 Break this problem into two subproblems by setting (x + -2) equal to 1.040833 and -1.040833.Subproblem 1
x + -2 = 1.040833 Simplifying x + -2 = 1.040833 Reorder the terms: -2 + x = 1.040833 Solving -2 + x = 1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.040833 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.040833 + 2 x = 1.040833 + 2 Combine like terms: 1.040833 + 2 = 3.040833 x = 3.040833 Simplifying x = 3.040833Subproblem 2
x + -2 = -1.040833 Simplifying x + -2 = -1.040833 Reorder the terms: -2 + x = -1.040833 Solving -2 + x = -1.040833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.040833 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.040833 + 2 x = -1.040833 + 2 Combine like terms: -1.040833 + 2 = 0.959167 x = 0.959167 Simplifying x = 0.959167Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.040833, 0.959167}
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