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Simplifying 0 = 12x2 + -72x + 80 Reorder the terms: 0 = 80 + -72x + 12x2 Solving 0 = 80 + -72x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + 72x + -12x2 = 80 + -72x + 12x2 + -80 + 72x + -12x2 Reorder the terms: -80 + 72x + -12x2 = 80 + -80 + -72x + 72x + 12x2 + -12x2 Combine like terms: 80 + -80 = 0 -80 + 72x + -12x2 = 0 + -72x + 72x + 12x2 + -12x2 -80 + 72x + -12x2 = -72x + 72x + 12x2 + -12x2 Combine like terms: -72x + 72x = 0 -80 + 72x + -12x2 = 0 + 12x2 + -12x2 -80 + 72x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -80 + 72x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-20 + 18x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-20 + 18x + -3x2)' equal to zero and attempt to solve: Simplifying -20 + 18x + -3x2 = 0 Solving -20 + 18x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 6.666666667 + -6x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + -6x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + -6x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + -6.666666667 -6x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 -6x + x2 = -6.666666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -6.666666667 + 9 Reorder the terms: 9 + -6x + x2 = -6.666666667 + 9 Combine like terms: -6.666666667 + 9 = 2.333333333 9 + -6x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -3) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -3 = 1.527525232 Simplifying x + -3 = 1.527525232 Reorder the terms: -3 + x = 1.527525232 Solving -3 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.527525232 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.527525232 + 3 x = 1.527525232 + 3 Combine like terms: 1.527525232 + 3 = 4.527525232 x = 4.527525232 Simplifying x = 4.527525232Subproblem 2
x + -3 = -1.527525232 Simplifying x + -3 = -1.527525232 Reorder the terms: -3 + x = -1.527525232 Solving -3 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.527525232 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.527525232 + 3 x = -1.527525232 + 3 Combine like terms: -1.527525232 + 3 = 1.472474768 x = 1.472474768 Simplifying x = 1.472474768Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.527525232, 1.472474768}Solution
x = {4.527525232, 1.472474768}
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