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Simplifying 4x2 + -23x + 11 = -7x Reorder the terms: 11 + -23x + 4x2 = -7x Solving 11 + -23x + 4x2 = -7x Solving for variable 'x'. Reorder the terms: 11 + -23x + 7x + 4x2 = -7x + 7x Combine like terms: -23x + 7x = -16x 11 + -16x + 4x2 = -7x + 7x Combine like terms: -7x + 7x = 0 11 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.75 + -4x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + -4x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + -4x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + -4x + x2 = 0 + -2.75 -4x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 -4x + x2 = -2.75 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 = -2.75 + 4 Reorder the terms: 4 + -4x + x2 = -2.75 + 4 Combine like terms: -2.75 + 4 = 1.25 4 + -4x + x2 = 1.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -2) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -2 = 1.118033989 Simplifying x + -2 = 1.118033989 Reorder the terms: -2 + x = 1.118033989 Solving -2 + x = 1.118033989 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 = 1.118033989 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.118033989 + 2 x = 1.118033989 + 2 Combine like terms: 1.118033989 + 2 = 3.118033989 x = 3.118033989 Simplifying x = 3.118033989Subproblem 2
x + -2 = -1.118033989 Simplifying x + -2 = -1.118033989 Reorder the terms: -2 + x = -1.118033989 Solving -2 + x = -1.118033989 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 = -1.118033989 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.118033989 + 2 x = -1.118033989 + 2 Combine like terms: -1.118033989 + 2 = 0.881966011 x = 0.881966011 Simplifying x = 0.881966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.118033989, 0.881966011}
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