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Simplifying 3x2 + 5x + -6 = -2x2 + -6x + 7 Reorder the terms: -6 + 5x + 3x2 = -2x2 + -6x + 7 Reorder the terms: -6 + 5x + 3x2 = 7 + -6x + -2x2 Solving -6 + 5x + 3x2 = 7 + -6x + -2x2 Solving for variable 'x'. Reorder the terms: -6 + -7 + 5x + 6x + 3x2 + 2x2 = 7 + -6x + -2x2 + -7 + 6x + 2x2 Combine like terms: -6 + -7 = -13 -13 + 5x + 6x + 3x2 + 2x2 = 7 + -6x + -2x2 + -7 + 6x + 2x2 Combine like terms: 5x + 6x = 11x -13 + 11x + 3x2 + 2x2 = 7 + -6x + -2x2 + -7 + 6x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 -13 + 11x + 5x2 = 7 + -6x + -2x2 + -7 + 6x + 2x2 Reorder the terms: -13 + 11x + 5x2 = 7 + -7 + -6x + 6x + -2x2 + 2x2 Combine like terms: 7 + -7 = 0 -13 + 11x + 5x2 = 0 + -6x + 6x + -2x2 + 2x2 -13 + 11x + 5x2 = -6x + 6x + -2x2 + 2x2 Combine like terms: -6x + 6x = 0 -13 + 11x + 5x2 = 0 + -2x2 + 2x2 -13 + 11x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -13 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 2.2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 2.2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 2.2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 2.2x + x2 = 0 + 2.6 2.2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 2.2x + x2 = 2.6 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 2.6 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 2.6 + 1.21 Combine like terms: 2.6 + 1.21 = 3.81 1.21 + 2.2x + x2 = 3.81 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 3.81 Calculate the square root of the right side: 1.95192213 Break this problem into two subproblems by setting (x + 1.1) equal to 1.95192213 and -1.95192213.Subproblem 1
x + 1.1 = 1.95192213 Simplifying x + 1.1 = 1.95192213 Reorder the terms: 1.1 + x = 1.95192213 Solving 1.1 + x = 1.95192213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.95192213 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.95192213 + -1.1 x = 1.95192213 + -1.1 Combine like terms: 1.95192213 + -1.1 = 0.85192213 x = 0.85192213 Simplifying x = 0.85192213Subproblem 2
x + 1.1 = -1.95192213 Simplifying x + 1.1 = -1.95192213 Reorder the terms: 1.1 + x = -1.95192213 Solving 1.1 + x = -1.95192213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.95192213 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.95192213 + -1.1 x = -1.95192213 + -1.1 Combine like terms: -1.95192213 + -1.1 = -3.05192213 x = -3.05192213 Simplifying x = -3.05192213Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.85192213, -3.05192213}
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