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Simplifying 4x2 + 17x + -11 = 0 Reorder the terms: -11 + 17x + 4x2 = 0 Solving -11 + 17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 4.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 4.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 4.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 4.25x + x2 = 0 + 2.75 4.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 4.25x + x2 = 2.75 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 2.75 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 2.75 + 4.515625 Combine like terms: 2.75 + 4.515625 = 7.265625 4.515625 + 4.25x + x2 = 7.265625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 7.265625 Calculate the square root of the right side: 2.695482332 Break this problem into two subproblems by setting (x + 2.125) equal to 2.695482332 and -2.695482332.Subproblem 1
x + 2.125 = 2.695482332 Simplifying x + 2.125 = 2.695482332 Reorder the terms: 2.125 + x = 2.695482332 Solving 2.125 + x = 2.695482332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.695482332 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.695482332 + -2.125 x = 2.695482332 + -2.125 Combine like terms: 2.695482332 + -2.125 = 0.570482332 x = 0.570482332 Simplifying x = 0.570482332Subproblem 2
x + 2.125 = -2.695482332 Simplifying x + 2.125 = -2.695482332 Reorder the terms: 2.125 + x = -2.695482332 Solving 2.125 + x = -2.695482332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.695482332 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.695482332 + -2.125 x = -2.695482332 + -2.125 Combine like terms: -2.695482332 + -2.125 = -4.820482332 x = -4.820482332 Simplifying x = -4.820482332Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.570482332, -4.820482332}
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