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Simplifying 4x2 + -5x + -6 = 11 Reorder the terms: -6 + -5x + 4x2 = 11 Solving -6 + -5x + 4x2 = 11 Solving for variable 'x'. Reorder the terms: -6 + -11 + -5x + 4x2 = 11 + -11 Combine like terms: -6 + -11 = -17 -17 + -5x + 4x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -17 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -1.25x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -1.25x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -1.25x + x2 = 0 + 4.25 -1.25x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -1.25x + x2 = 4.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 4.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 4.25 + 0.390625 Combine like terms: 4.25 + 0.390625 = 4.640625 0.390625 + -1.25x + x2 = 4.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + -0.625) equal to 2.154210992 and -2.154210992.Subproblem 1
x + -0.625 = 2.154210992 Simplifying x + -0.625 = 2.154210992 Reorder the terms: -0.625 + x = 2.154210992 Solving -0.625 + x = 2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 2.154210992 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 2.154210992 + 0.625 x = 2.154210992 + 0.625 Combine like terms: 2.154210992 + 0.625 = 2.779210992 x = 2.779210992 Simplifying x = 2.779210992Subproblem 2
x + -0.625 = -2.154210992 Simplifying x + -0.625 = -2.154210992 Reorder the terms: -0.625 + x = -2.154210992 Solving -0.625 + x = -2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -2.154210992 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -2.154210992 + 0.625 x = -2.154210992 + 0.625 Combine like terms: -2.154210992 + 0.625 = -1.529210992 x = -1.529210992 Simplifying x = -1.529210992Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.779210992, -1.529210992}
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