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Simplifying (2x2 + -5x + 4) + (3x2 + -8x) = 0 Reorder the terms: (4 + -5x + 2x2) + (3x2 + -8x) = 0 Remove parenthesis around (4 + -5x + 2x2) 4 + -5x + 2x2 + (3x2 + -8x) = 0 Reorder the terms: 4 + -5x + 2x2 + (-8x + 3x2) = 0 Remove parenthesis around (-8x + 3x2) 4 + -5x + 2x2 + -8x + 3x2 = 0 Reorder the terms: 4 + -5x + -8x + 2x2 + 3x2 = 0 Combine like terms: -5x + -8x = -13x 4 + -13x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 4 + -13x + 5x2 = 0 Solving 4 + -13x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -2.6x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.6x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.6x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.6x + x2 = 0 + -0.8 -2.6x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.6x + x2 = -0.8 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = -0.8 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = -0.8 + 1.69 Combine like terms: -0.8 + 1.69 = 0.89 1.69 + -2.6x + x2 = 0.89 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -1.3) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -1.3 = 0.943398113 Simplifying x + -1.3 = 0.943398113 Reorder the terms: -1.3 + x = 0.943398113 Solving -1.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = 0.943398113 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = 0.943398113 + 1.3 x = 0.943398113 + 1.3 Combine like terms: 0.943398113 + 1.3 = 2.243398113 x = 2.243398113 Simplifying x = 2.243398113Subproblem 2
x + -1.3 = -0.943398113 Simplifying x + -1.3 = -0.943398113 Reorder the terms: -1.3 + x = -0.943398113 Solving -1.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + x = -0.943398113 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + x = -0.943398113 + 1.3 x = -0.943398113 + 1.3 Combine like terms: -0.943398113 + 1.3 = 0.356601887 x = 0.356601887 Simplifying x = 0.356601887Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.243398113, 0.356601887}
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