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Simplifying 8x2 + -13x + 2 = 3x2 + 2x + -4 Reorder the terms: 2 + -13x + 8x2 = 3x2 + 2x + -4 Reorder the terms: 2 + -13x + 8x2 = -4 + 2x + 3x2 Solving 2 + -13x + 8x2 = -4 + 2x + 3x2 Solving for variable 'x'. Reorder the terms: 2 + 4 + -13x + -2x + 8x2 + -3x2 = -4 + 2x + 3x2 + 4 + -2x + -3x2 Combine like terms: 2 + 4 = 6 6 + -13x + -2x + 8x2 + -3x2 = -4 + 2x + 3x2 + 4 + -2x + -3x2 Combine like terms: -13x + -2x = -15x 6 + -15x + 8x2 + -3x2 = -4 + 2x + 3x2 + 4 + -2x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 6 + -15x + 5x2 = -4 + 2x + 3x2 + 4 + -2x + -3x2 Reorder the terms: 6 + -15x + 5x2 = -4 + 4 + 2x + -2x + 3x2 + -3x2 Combine like terms: -4 + 4 = 0 6 + -15x + 5x2 = 0 + 2x + -2x + 3x2 + -3x2 6 + -15x + 5x2 = 2x + -2x + 3x2 + -3x2 Combine like terms: 2x + -2x = 0 6 + -15x + 5x2 = 0 + 3x2 + -3x2 6 + -15x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 6 + -15x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + -3x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -3x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -3x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -3x + x2 = 0 + -1.2 -3x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -3x + x2 = -1.2 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.2 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.2 + 2.25 Combine like terms: -1.2 + 2.25 = 1.05 2.25 + -3x + x2 = 1.05 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.05 Calculate the square root of the right side: 1.024695077 Break this problem into two subproblems by setting (x + -1.5) equal to 1.024695077 and -1.024695077.Subproblem 1
x + -1.5 = 1.024695077 Simplifying x + -1.5 = 1.024695077 Reorder the terms: -1.5 + x = 1.024695077 Solving -1.5 + x = 1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.024695077 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.024695077 + 1.5 x = 1.024695077 + 1.5 Combine like terms: 1.024695077 + 1.5 = 2.524695077 x = 2.524695077 Simplifying x = 2.524695077Subproblem 2
x + -1.5 = -1.024695077 Simplifying x + -1.5 = -1.024695077 Reorder the terms: -1.5 + x = -1.024695077 Solving -1.5 + x = -1.024695077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.024695077 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.024695077 + 1.5 x = -1.024695077 + 1.5 Combine like terms: -1.024695077 + 1.5 = 0.475304923 x = 0.475304923 Simplifying x = 0.475304923Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.524695077, 0.475304923}
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