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Simplifying 12x2 + 48x + -95 = 0 Reorder the terms: -95 + 48x + 12x2 = 0 Solving -95 + 48x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -7.916666667 + 4x + x2 = 0 Move the constant term to the right: Add '7.916666667' to each side of the equation. -7.916666667 + 4x + 7.916666667 + x2 = 0 + 7.916666667 Reorder the terms: -7.916666667 + 7.916666667 + 4x + x2 = 0 + 7.916666667 Combine like terms: -7.916666667 + 7.916666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 7.916666667 4x + x2 = 0 + 7.916666667 Combine like terms: 0 + 7.916666667 = 7.916666667 4x + x2 = 7.916666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7.916666667 + 4 Reorder the terms: 4 + 4x + x2 = 7.916666667 + 4 Combine like terms: 7.916666667 + 4 = 11.916666667 4 + 4x + x2 = 11.916666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 11.916666667 Calculate the square root of the right side: 3.45205253 Break this problem into two subproblems by setting (x + 2) equal to 3.45205253 and -3.45205253.Subproblem 1
x + 2 = 3.45205253 Simplifying x + 2 = 3.45205253 Reorder the terms: 2 + x = 3.45205253 Solving 2 + x = 3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.45205253 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.45205253 + -2 x = 3.45205253 + -2 Combine like terms: 3.45205253 + -2 = 1.45205253 x = 1.45205253 Simplifying x = 1.45205253Subproblem 2
x + 2 = -3.45205253 Simplifying x + 2 = -3.45205253 Reorder the terms: 2 + x = -3.45205253 Solving 2 + x = -3.45205253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.45205253 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.45205253 + -2 x = -3.45205253 + -2 Combine like terms: -3.45205253 + -2 = -5.45205253 x = -5.45205253 Simplifying x = -5.45205253Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.45205253, -5.45205253}
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