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Simplifying -6x2 + -23x + -4 = 0 Reorder the terms: -4 + -23x + -6x2 = 0 Solving -4 + -23x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 23x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 23x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + 23x + 6x2 = 0 Solving 4 + 23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 3.833333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 3.833333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 3.833333333x + x2 = 0 + -0.6666666667 3.833333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 3.833333333x + x2 = -0.6666666667 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 = -0.6666666667 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = -0.6666666667 + 3.673611112 Combine like terms: -0.6666666667 + 3.673611112 = 3.0069444453 3.673611112 + 3.833333333x + x2 = 3.0069444453 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 3.0069444453 Calculate the square root of the right side: 1.734054337 Break this problem into two subproblems by setting (x + 1.916666667) equal to 1.734054337 and -1.734054337.Subproblem 1
x + 1.916666667 = 1.734054337 Simplifying x + 1.916666667 = 1.734054337 Reorder the terms: 1.916666667 + x = 1.734054337 Solving 1.916666667 + x = 1.734054337 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 = 1.734054337 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 1.734054337 + -1.916666667 x = 1.734054337 + -1.916666667 Combine like terms: 1.734054337 + -1.916666667 = -0.18261233 x = -0.18261233 Simplifying x = -0.18261233Subproblem 2
x + 1.916666667 = -1.734054337 Simplifying x + 1.916666667 = -1.734054337 Reorder the terms: 1.916666667 + x = -1.734054337 Solving 1.916666667 + x = -1.734054337 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 = -1.734054337 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -1.734054337 + -1.916666667 x = -1.734054337 + -1.916666667 Combine like terms: -1.734054337 + -1.916666667 = -3.650721004 x = -3.650721004 Simplifying x = -3.650721004Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.18261233, -3.650721004}Solution
x = {-0.18261233, -3.650721004}
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