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Simplifying x2 + 6x + -1.35 = 2x2 + 2x + 2.56 Reorder the terms: -1.35 + 6x + x2 = 2x2 + 2x + 2.56 Reorder the terms: -1.35 + 6x + x2 = 2.56 + 2x + 2x2 Solving -1.35 + 6x + x2 = 2.56 + 2x + 2x2 Solving for variable 'x'. Reorder the terms: -1.35 + -2.56 + 6x + -2x + x2 + -2x2 = 2.56 + 2x + 2x2 + -2.56 + -2x + -2x2 Combine like terms: -1.35 + -2.56 = -3.91 -3.91 + 6x + -2x + x2 + -2x2 = 2.56 + 2x + 2x2 + -2.56 + -2x + -2x2 Combine like terms: 6x + -2x = 4x -3.91 + 4x + x2 + -2x2 = 2.56 + 2x + 2x2 + -2.56 + -2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -3.91 + 4x + -1x2 = 2.56 + 2x + 2x2 + -2.56 + -2x + -2x2 Reorder the terms: -3.91 + 4x + -1x2 = 2.56 + -2.56 + 2x + -2x + 2x2 + -2x2 Combine like terms: 2.56 + -2.56 = 0.00 -3.91 + 4x + -1x2 = 0.00 + 2x + -2x + 2x2 + -2x2 -3.91 + 4x + -1x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 -3.91 + 4x + -1x2 = 0 + 2x2 + -2x2 -3.91 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3.91 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3.91 + -4x + x2 = 0 Move the constant term to the right: Add '-3.91' to each side of the equation. 3.91 + -4x + -3.91 + x2 = 0 + -3.91 Reorder the terms: 3.91 + -3.91 + -4x + x2 = 0 + -3.91 Combine like terms: 3.91 + -3.91 = 0.00 0.00 + -4x + x2 = 0 + -3.91 -4x + x2 = 0 + -3.91 Combine like terms: 0 + -3.91 = -3.91 -4x + x2 = -3.91 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.91 + 4 Reorder the terms: 4 + -4x + x2 = -3.91 + 4 Combine like terms: -3.91 + 4 = 0.09 4 + -4x + x2 = 0.09 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (x + -2) equal to 0.3 and -0.3.Subproblem 1
x + -2 = 0.3 Simplifying x + -2 = 0.3 Reorder the terms: -2 + x = 0.3 Solving -2 + x = 0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.3 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.3 + 2 x = 0.3 + 2 Combine like terms: 0.3 + 2 = 2.3 x = 2.3 Simplifying x = 2.3Subproblem 2
x + -2 = -0.3 Simplifying x + -2 = -0.3 Reorder the terms: -2 + x = -0.3 Solving -2 + x = -0.3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.3 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.3 + 2 x = -0.3 + 2 Combine like terms: -0.3 + 2 = 1.7 x = 1.7 Simplifying x = 1.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3, 1.7}
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