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Simplifying 12x2 + 46x = 22 Reorder the terms: 46x + 12x2 = 22 Solving 46x + 12x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 46x + 12x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 46x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 23x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 23x + 6x2)' equal to zero and attempt to solve: Simplifying -11 + 23x + 6x2 = 0 Solving -11 + 23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 3.833333333x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 3.833333333x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 3.833333333x + x2 = 0 + 1.833333333 3.833333333x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 3.833333333x + x2 = 1.833333333 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = 1.833333333 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = 1.833333333 + 3.673611112 Combine like terms: 1.833333333 + 3.673611112 = 5.506944445 3.673611112 + 3.833333333x + x2 = 5.506944445 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 5.506944445 Calculate the square root of the right side: 2.346687974 Break this problem into two subproblems by setting (x + 1.916666667) equal to 2.346687974 and -2.346687974.Subproblem 1
x + 1.916666667 = 2.346687974 Simplifying x + 1.916666667 = 2.346687974 Reorder the terms: 1.916666667 + x = 2.346687974 Solving 1.916666667 + x = 2.346687974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 2.346687974 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 2.346687974 + -1.916666667 x = 2.346687974 + -1.916666667 Combine like terms: 2.346687974 + -1.916666667 = 0.430021307 x = 0.430021307 Simplifying x = 0.430021307Subproblem 2
x + 1.916666667 = -2.346687974 Simplifying x + 1.916666667 = -2.346687974 Reorder the terms: 1.916666667 + x = -2.346687974 Solving 1.916666667 + x = -2.346687974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -2.346687974 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -2.346687974 + -1.916666667 x = -2.346687974 + -1.916666667 Combine like terms: -2.346687974 + -1.916666667 = -4.263354641 x = -4.263354641 Simplifying x = -4.263354641Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.430021307, -4.263354641}Solution
x = {0.430021307, -4.263354641}
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