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Simplifying 4x2 = -13x + 11 Reorder the terms: 4x2 = 11 + -13x Solving 4x2 = 11 + -13x Solving for variable 'x'. Reorder the terms: -11 + 13x + 4x2 = 11 + -13x + -11 + 13x Reorder the terms: -11 + 13x + 4x2 = 11 + -11 + -13x + 13x Combine like terms: 11 + -11 = 0 -11 + 13x + 4x2 = 0 + -13x + 13x -11 + 13x + 4x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -11 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 3.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 3.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 3.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 3.25x + x2 = 0 + 2.75 3.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 3.25x + x2 = 2.75 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 2.75 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 2.75 + 2.640625 Combine like terms: 2.75 + 2.640625 = 5.390625 2.640625 + 3.25x + x2 = 5.390625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 5.390625 Calculate the square root of the right side: 2.321771953 Break this problem into two subproblems by setting (x + 1.625) equal to 2.321771953 and -2.321771953.Subproblem 1
x + 1.625 = 2.321771953 Simplifying x + 1.625 = 2.321771953 Reorder the terms: 1.625 + x = 2.321771953 Solving 1.625 + x = 2.321771953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 2.321771953 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.321771953 + -1.625 x = 2.321771953 + -1.625 Combine like terms: 2.321771953 + -1.625 = 0.696771953 x = 0.696771953 Simplifying x = 0.696771953Subproblem 2
x + 1.625 = -2.321771953 Simplifying x + 1.625 = -2.321771953 Reorder the terms: 1.625 + x = -2.321771953 Solving 1.625 + x = -2.321771953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -2.321771953 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.321771953 + -1.625 x = -2.321771953 + -1.625 Combine like terms: -2.321771953 + -1.625 = -3.946771953 x = -3.946771953 Simplifying x = -3.946771953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696771953, -3.946771953}
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