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Simplifying (2x2 + -2x + 11) + (3x2 + 5x + -46) = 0 Reorder the terms: (11 + -2x + 2x2) + (3x2 + 5x + -46) = 0 Remove parenthesis around (11 + -2x + 2x2) 11 + -2x + 2x2 + (3x2 + 5x + -46) = 0 Reorder the terms: 11 + -2x + 2x2 + (-46 + 5x + 3x2) = 0 Remove parenthesis around (-46 + 5x + 3x2) 11 + -2x + 2x2 + -46 + 5x + 3x2 = 0 Reorder the terms: 11 + -46 + -2x + 5x + 2x2 + 3x2 = 0 Combine like terms: 11 + -46 = -35 -35 + -2x + 5x + 2x2 + 3x2 = 0 Combine like terms: -2x + 5x = 3x -35 + 3x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -35 + 3x + 5x2 = 0 Solving -35 + 3x + 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'. -7 + 0.6x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.6x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 0.6x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.6x + x2 = 0 + 7 0.6x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.6x + x2 = 7 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 7 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 7 + 0.09 Combine like terms: 7 + 0.09 = 7.09 0.09 + 0.6x + x2 = 7.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 7.09 Calculate the square root of the right side: 2.662705391 Break this problem into two subproblems by setting (x + 0.3) equal to 2.662705391 and -2.662705391.Subproblem 1
x + 0.3 = 2.662705391 Simplifying x + 0.3 = 2.662705391 Reorder the terms: 0.3 + x = 2.662705391 Solving 0.3 + x = 2.662705391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.662705391 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.662705391 + -0.3 x = 2.662705391 + -0.3 Combine like terms: 2.662705391 + -0.3 = 2.362705391 x = 2.362705391 Simplifying x = 2.362705391Subproblem 2
x + 0.3 = -2.662705391 Simplifying x + 0.3 = -2.662705391 Reorder the terms: 0.3 + x = -2.662705391 Solving 0.3 + x = -2.662705391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.662705391 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.662705391 + -0.3 x = -2.662705391 + -0.3 Combine like terms: -2.662705391 + -0.3 = -2.962705391 x = -2.962705391 Simplifying x = -2.962705391Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.362705391, -2.962705391}
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