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Simplifying 0 = 12x2 + -48x + 20 Reorder the terms: 0 = 20 + -48x + 12x2 Solving 0 = 20 + -48x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 48x + -12x2 = 20 + -48x + 12x2 + -20 + 48x + -12x2 Reorder the terms: -20 + 48x + -12x2 = 20 + -20 + -48x + 48x + 12x2 + -12x2 Combine like terms: 20 + -20 = 0 -20 + 48x + -12x2 = 0 + -48x + 48x + 12x2 + -12x2 -20 + 48x + -12x2 = -48x + 48x + 12x2 + -12x2 Combine like terms: -48x + 48x = 0 -20 + 48x + -12x2 = 0 + 12x2 + -12x2 -20 + 48x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -20 + 48x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 12x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 12x + -3x2)' equal to zero and attempt to solve: Simplifying -5 + 12x + -3x2 = 0 Solving -5 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -4x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -4x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -1.666666667 -4x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -4x + x2 = -1.666666667 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 = -1.666666667 + 4 Reorder the terms: 4 + -4x + x2 = -1.666666667 + 4 Combine like terms: -1.666666667 + 4 = 2.333333333 4 + -4x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -2) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -2 = 1.527525232 Simplifying x + -2 = 1.527525232 Reorder the terms: -2 + x = 1.527525232 Solving -2 + x = 1.527525232 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 = 1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.527525232 + 2 x = 1.527525232 + 2 Combine like terms: 1.527525232 + 2 = 3.527525232 x = 3.527525232 Simplifying x = 3.527525232Subproblem 2
x + -2 = -1.527525232 Simplifying x + -2 = -1.527525232 Reorder the terms: -2 + x = -1.527525232 Solving -2 + x = -1.527525232 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 = -1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.527525232 + 2 x = -1.527525232 + 2 Combine like terms: -1.527525232 + 2 = 0.472474768 x = 0.472474768 Simplifying x = 0.472474768Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.527525232, 0.472474768}Solution
x = {3.527525232, 0.472474768}
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