12x^2-76x+88=0

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Solution for 12x^2-76x+88=0 equation:


Simplifying
12x2 + -76x + 88 = 0

Reorder the terms:
88 + -76x + 12x2 = 0

Solving
88 + -76x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(22 + -19x + 3x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(22 + -19x + 3x2)' equal to zero and attempt to solve: Simplifying 22 + -19x + 3x2 = 0 Solving 22 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.333333333 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -6.333333333x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -6.333333333x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -6.333333333x + x2 = 0 + -7.333333333 -6.333333333x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -6.333333333x + x2 = -7.333333333 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = -7.333333333 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = -7.333333333 + 10.02777778 Combine like terms: -7.333333333 + 10.02777778 = 2.694444447 10.02777778 + -6.333333333x + x2 = 2.694444447 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 2.694444447 Calculate the square root of the right side: 1.641476301 Break this problem into two subproblems by setting (x + -3.166666667) equal to 1.641476301 and -1.641476301.

Subproblem 1

x + -3.166666667 = 1.641476301 Simplifying x + -3.166666667 = 1.641476301 Reorder the terms: -3.166666667 + x = 1.641476301 Solving -3.166666667 + x = 1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 1.641476301 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 1.641476301 + 3.166666667 x = 1.641476301 + 3.166666667 Combine like terms: 1.641476301 + 3.166666667 = 4.808142968 x = 4.808142968 Simplifying x = 4.808142968

Subproblem 2

x + -3.166666667 = -1.641476301 Simplifying x + -3.166666667 = -1.641476301 Reorder the terms: -3.166666667 + x = -1.641476301 Solving -3.166666667 + x = -1.641476301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -1.641476301 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -1.641476301 + 3.166666667 x = -1.641476301 + 3.166666667 Combine like terms: -1.641476301 + 3.166666667 = 1.525190366 x = 1.525190366 Simplifying x = 1.525190366

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.808142968, 1.525190366}

Solution

x = {4.808142968, 1.525190366}

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