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Simplifying -12x2 + -70x + -13 = 0 Reorder the terms: -13 + -70x + -12x2 = 0 Solving -13 + -70x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 70x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 70x + 12x2)' equal to zero and attempt to solve: Simplifying 13 + 70x + 12x2 = 0 Solving 13 + 70x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.083333333 + 5.833333333x + x2 = 0 Move the constant term to the right: Add '-1.083333333' to each side of the equation. 1.083333333 + 5.833333333x + -1.083333333 + x2 = 0 + -1.083333333 Reorder the terms: 1.083333333 + -1.083333333 + 5.833333333x + x2 = 0 + -1.083333333 Combine like terms: 1.083333333 + -1.083333333 = 0.000000000 0.000000000 + 5.833333333x + x2 = 0 + -1.083333333 5.833333333x + x2 = 0 + -1.083333333 Combine like terms: 0 + -1.083333333 = -1.083333333 5.833333333x + x2 = -1.083333333 The x term is 5.833333333x. Take half its coefficient (2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. 5.833333333x + 8.506944446 + x2 = -1.083333333 + 8.506944446 Reorder the terms: 8.506944446 + 5.833333333x + x2 = -1.083333333 + 8.506944446 Combine like terms: -1.083333333 + 8.506944446 = 7.423611113 8.506944446 + 5.833333333x + x2 = 7.423611113 Factor a perfect square on the left side: (x + 2.916666667)(x + 2.916666667) = 7.423611113 Calculate the square root of the right side: 2.724630454 Break this problem into two subproblems by setting (x + 2.916666667) equal to 2.724630454 and -2.724630454.Subproblem 1
x + 2.916666667 = 2.724630454 Simplifying x + 2.916666667 = 2.724630454 Reorder the terms: 2.916666667 + x = 2.724630454 Solving 2.916666667 + x = 2.724630454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = 2.724630454 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = 2.724630454 + -2.916666667 x = 2.724630454 + -2.916666667 Combine like terms: 2.724630454 + -2.916666667 = -0.192036213 x = -0.192036213 Simplifying x = -0.192036213Subproblem 2
x + 2.916666667 = -2.724630454 Simplifying x + 2.916666667 = -2.724630454 Reorder the terms: 2.916666667 + x = -2.724630454 Solving 2.916666667 + x = -2.724630454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = -2.724630454 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = -2.724630454 + -2.916666667 x = -2.724630454 + -2.916666667 Combine like terms: -2.724630454 + -2.916666667 = -5.641297121 x = -5.641297121 Simplifying x = -5.641297121Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.192036213, -5.641297121}Solution
x = {-0.192036213, -5.641297121}
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