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Simplifying 12x2 + -28x + -13 = 0 Reorder the terms: -13 + -28x + 12x2 = 0 Solving -13 + -28x + 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'. -1.083333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + -2.333333333x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + -2.333333333x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 1.083333333 -2.333333333x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 -2.333333333x + x2 = 1.083333333 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 1.083333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 1.083333333 + 1.361111112 Combine like terms: 1.083333333 + 1.361111112 = 2.444444445 1.361111112 + -2.333333333x + x2 = 2.444444445 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 2.444444445 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.56347192 and -1.56347192.Subproblem 1
x + -1.166666667 = 1.56347192 Simplifying x + -1.166666667 = 1.56347192 Reorder the terms: -1.166666667 + x = 1.56347192 Solving -1.166666667 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.56347192 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.56347192 + 1.166666667 x = 1.56347192 + 1.166666667 Combine like terms: 1.56347192 + 1.166666667 = 2.730138587 x = 2.730138587 Simplifying x = 2.730138587Subproblem 2
x + -1.166666667 = -1.56347192 Simplifying x + -1.166666667 = -1.56347192 Reorder the terms: -1.166666667 + x = -1.56347192 Solving -1.166666667 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.56347192 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.56347192 + 1.166666667 x = -1.56347192 + 1.166666667 Combine like terms: -1.56347192 + 1.166666667 = -0.396805253 x = -0.396805253 Simplifying x = -0.396805253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.730138587, -0.396805253}
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