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Simplifying 6x2 + -5x = 3 + -5x2 Reorder the terms: -5x + 6x2 = 3 + -5x2 Solving -5x + 6x2 = 3 + -5x2 Solving for variable 'x'. Reorder the terms: -3 + -5x + 6x2 + 5x2 = 3 + -5x2 + -3 + 5x2 Combine like terms: 6x2 + 5x2 = 11x2 -3 + -5x + 11x2 = 3 + -5x2 + -3 + 5x2 Reorder the terms: -3 + -5x + 11x2 = 3 + -3 + -5x2 + 5x2 Combine like terms: 3 + -3 = 0 -3 + -5x + 11x2 = 0 + -5x2 + 5x2 -3 + -5x + 11x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -3 + -5x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.4545454545x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.4545454545x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.4545454545x + x2 = 0 + 0.2727272727 -0.4545454545x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.4545454545x + x2 = 0.2727272727 The x term is -0.4545454545x. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545x + 0.05165289257 + x2 = 0.2727272727 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 0.2727272727 + 0.05165289257 Combine like terms: 0.2727272727 + 0.05165289257 = 0.32438016527 0.05165289257 + -0.4545454545x + x2 = 0.32438016527 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 0.32438016527 Calculate the square root of the right side: 0.569543822 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 0.569543822 and -0.569543822.Subproblem 1
x + -0.2272727273 = 0.569543822 Simplifying x + -0.2272727273 = 0.569543822 Reorder the terms: -0.2272727273 + x = 0.569543822 Solving -0.2272727273 + x = 0.569543822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = 0.569543822 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 0.569543822 + 0.2272727273 x = 0.569543822 + 0.2272727273 Combine like terms: 0.569543822 + 0.2272727273 = 0.7968165493 x = 0.7968165493 Simplifying x = 0.7968165493Subproblem 2
x + -0.2272727273 = -0.569543822 Simplifying x + -0.2272727273 = -0.569543822 Reorder the terms: -0.2272727273 + x = -0.569543822 Solving -0.2272727273 + x = -0.569543822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = -0.569543822 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -0.569543822 + 0.2272727273 x = -0.569543822 + 0.2272727273 Combine like terms: -0.569543822 + 0.2272727273 = -0.3422710947 x = -0.3422710947 Simplifying x = -0.3422710947Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7968165493, -0.3422710947}
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