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Simplifying 4x2 + -31x + -41 = -7x + 6 Reorder the terms: -41 + -31x + 4x2 = -7x + 6 Reorder the terms: -41 + -31x + 4x2 = 6 + -7x Solving -41 + -31x + 4x2 = 6 + -7x Solving for variable 'x'. Reorder the terms: -41 + -6 + -31x + 7x + 4x2 = 6 + -7x + -6 + 7x Combine like terms: -41 + -6 = -47 -47 + -31x + 7x + 4x2 = 6 + -7x + -6 + 7x Combine like terms: -31x + 7x = -24x -47 + -24x + 4x2 = 6 + -7x + -6 + 7x Reorder the terms: -47 + -24x + 4x2 = 6 + -6 + -7x + 7x Combine like terms: 6 + -6 = 0 -47 + -24x + 4x2 = 0 + -7x + 7x -47 + -24x + 4x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -47 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.75 + -6x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + -6x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + -6x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + -6x + x2 = 0 + 11.75 -6x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 -6x + x2 = 11.75 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 = 11.75 + 9 Reorder the terms: 9 + -6x + x2 = 11.75 + 9 Combine like terms: 11.75 + 9 = 20.75 9 + -6x + x2 = 20.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 20.75 Calculate the square root of the right side: 4.55521679 Break this problem into two subproblems by setting (x + -3) equal to 4.55521679 and -4.55521679.Subproblem 1
x + -3 = 4.55521679 Simplifying x + -3 = 4.55521679 Reorder the terms: -3 + x = 4.55521679 Solving -3 + x = 4.55521679 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 = 4.55521679 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.55521679 + 3 x = 4.55521679 + 3 Combine like terms: 4.55521679 + 3 = 7.55521679 x = 7.55521679 Simplifying x = 7.55521679Subproblem 2
x + -3 = -4.55521679 Simplifying x + -3 = -4.55521679 Reorder the terms: -3 + x = -4.55521679 Solving -3 + x = -4.55521679 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 = -4.55521679 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.55521679 + 3 x = -4.55521679 + 3 Combine like terms: -4.55521679 + 3 = -1.55521679 x = -1.55521679 Simplifying x = -1.55521679Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.55521679, -1.55521679}
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