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Simplifying 4x2 + 6x + -11 = 10 + -13x Reorder the terms: -11 + 6x + 4x2 = 10 + -13x Solving -11 + 6x + 4x2 = 10 + -13x Solving for variable 'x'. Reorder the terms: -11 + -10 + 6x + 13x + 4x2 = 10 + -13x + -10 + 13x Combine like terms: -11 + -10 = -21 -21 + 6x + 13x + 4x2 = 10 + -13x + -10 + 13x Combine like terms: 6x + 13x = 19x -21 + 19x + 4x2 = 10 + -13x + -10 + 13x Reorder the terms: -21 + 19x + 4x2 = 10 + -10 + -13x + 13x Combine like terms: 10 + -10 = 0 -21 + 19x + 4x2 = 0 + -13x + 13x -21 + 19x + 4x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -21 + 19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 4.75x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 4.75x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 4.75x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 4.75x + x2 = 0 + 5.25 4.75x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 4.75x + x2 = 5.25 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 5.25 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 5.25 + 5.640625 Combine like terms: 5.25 + 5.640625 = 10.890625 5.640625 + 4.75x + x2 = 10.890625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + 2.375) equal to 3.300094696 and -3.300094696.Subproblem 1
x + 2.375 = 3.300094696 Simplifying x + 2.375 = 3.300094696 Reorder the terms: 2.375 + x = 3.300094696 Solving 2.375 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 3.300094696 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.300094696 + -2.375 x = 3.300094696 + -2.375 Combine like terms: 3.300094696 + -2.375 = 0.925094696 x = 0.925094696 Simplifying x = 0.925094696Subproblem 2
x + 2.375 = -3.300094696 Simplifying x + 2.375 = -3.300094696 Reorder the terms: 2.375 + x = -3.300094696 Solving 2.375 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -3.300094696 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.300094696 + -2.375 x = -3.300094696 + -2.375 Combine like terms: -3.300094696 + -2.375 = -5.675094696 x = -5.675094696 Simplifying x = -5.675094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.925094696, -5.675094696}
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