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Simplifying -12x2 + -28x + 12 = 0 Reorder the terms: 12 + -28x + -12x2 = 0 Solving 12 + -28x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -7x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -7x + -3x2)' equal to zero and attempt to solve: Simplifying 3 + -7x + -3x2 = 0 Solving 3 + -7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.333333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2.333333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.333333333x + x2 = 0 + 1 2.333333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.333333333x + x2 = 1 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 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 1 + 1.361111112 Combine like terms: 1 + 1.361111112 = 2.361111112 1.361111112 + 2.333333333x + x2 = 2.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 2.361111112 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.536590743 and -1.536590743.Subproblem 1
x + 1.166666667 = 1.536590743 Simplifying x + 1.166666667 = 1.536590743 Reorder the terms: 1.166666667 + x = 1.536590743 Solving 1.166666667 + x = 1.536590743 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 = 1.536590743 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.536590743 + -1.166666667 x = 1.536590743 + -1.166666667 Combine like terms: 1.536590743 + -1.166666667 = 0.369924076 x = 0.369924076 Simplifying x = 0.369924076Subproblem 2
x + 1.166666667 = -1.536590743 Simplifying x + 1.166666667 = -1.536590743 Reorder the terms: 1.166666667 + x = -1.536590743 Solving 1.166666667 + x = -1.536590743 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 = -1.536590743 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.536590743 + -1.166666667 x = -1.536590743 + -1.166666667 Combine like terms: -1.536590743 + -1.166666667 = -2.70325741 x = -2.70325741 Simplifying x = -2.70325741Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.369924076, -2.70325741}Solution
x = {0.369924076, -2.70325741}
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