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Simplifying 12x2 + -196 = 28x Reorder the terms: -196 + 12x2 = 28x Solving -196 + 12x2 = 28x Solving for variable 'x'. Reorder the terms: -196 + -28x + 12x2 = 28x + -28x Combine like terms: 28x + -28x = 0 -196 + -28x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-49 + -7x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-49 + -7x + 3x2)' equal to zero and attempt to solve: Simplifying -49 + -7x + 3x2 = 0 Solving -49 + -7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -16.33333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '16.33333333' to each side of the equation. -16.33333333 + -2.333333333x + 16.33333333 + x2 = 0 + 16.33333333 Reorder the terms: -16.33333333 + 16.33333333 + -2.333333333x + x2 = 0 + 16.33333333 Combine like terms: -16.33333333 + 16.33333333 = 0.00000000 0.00000000 + -2.333333333x + x2 = 0 + 16.33333333 -2.333333333x + x2 = 0 + 16.33333333 Combine like terms: 0 + 16.33333333 = 16.33333333 -2.333333333x + x2 = 16.33333333 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 = 16.33333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 16.33333333 + 1.361111112 Combine like terms: 16.33333333 + 1.361111112 = 17.694444442 1.361111112 + -2.333333333x + x2 = 17.694444442 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 17.694444442 Calculate the square root of the right side: 4.206476488 Break this problem into two subproblems by setting (x + -1.166666667) equal to 4.206476488 and -4.206476488.Subproblem 1
x + -1.166666667 = 4.206476488 Simplifying x + -1.166666667 = 4.206476488 Reorder the terms: -1.166666667 + x = 4.206476488 Solving -1.166666667 + x = 4.206476488 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 = 4.206476488 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 4.206476488 + 1.166666667 x = 4.206476488 + 1.166666667 Combine like terms: 4.206476488 + 1.166666667 = 5.373143155 x = 5.373143155 Simplifying x = 5.373143155Subproblem 2
x + -1.166666667 = -4.206476488 Simplifying x + -1.166666667 = -4.206476488 Reorder the terms: -1.166666667 + x = -4.206476488 Solving -1.166666667 + x = -4.206476488 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 = -4.206476488 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -4.206476488 + 1.166666667 x = -4.206476488 + 1.166666667 Combine like terms: -4.206476488 + 1.166666667 = -3.039809821 x = -3.039809821 Simplifying x = -3.039809821Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.373143155, -3.039809821}Solution
x = {5.373143155, -3.039809821}
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