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Simplifying 4x2 + -24x + 36 = 22 Reorder the terms: 36 + -24x + 4x2 = 22 Solving 36 + -24x + 4x2 = 22 Solving for variable 'x'. Reorder the terms: 36 + -22 + -24x + 4x2 = 22 + -22 Combine like terms: 36 + -22 = 14 14 + -24x + 4x2 = 22 + -22 Combine like terms: 22 + -22 = 0 14 + -24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + -12x + 2x2 = 0 Solving 7 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -6x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -6x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -6x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -6x + x2 = 0 + -3.5 -6x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -6x + x2 = -3.5 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 = -3.5 + 9 Reorder the terms: 9 + -6x + x2 = -3.5 + 9 Combine like terms: -3.5 + 9 = 5.5 9 + -6x + x2 = 5.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -3) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -3 = 2.34520788 Simplifying x + -3 = 2.34520788 Reorder the terms: -3 + x = 2.34520788 Solving -3 + x = 2.34520788 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 = 2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.34520788 + 3 x = 2.34520788 + 3 Combine like terms: 2.34520788 + 3 = 5.34520788 x = 5.34520788 Simplifying x = 5.34520788Subproblem 2
x + -3 = -2.34520788 Simplifying x + -3 = -2.34520788 Reorder the terms: -3 + x = -2.34520788 Solving -3 + x = -2.34520788 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 = -2.34520788 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.34520788 + 3 x = -2.34520788 + 3 Combine like terms: -2.34520788 + 3 = 0.65479212 x = 0.65479212 Simplifying x = 0.65479212Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.34520788, 0.65479212}Solution
x = {5.34520788, 0.65479212}
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