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Simplifying (x2 + -5x + 6) + (-4x2 + 2x + 7) = 0 Reorder the terms: (6 + -5x + x2) + (-4x2 + 2x + 7) = 0 Remove parenthesis around (6 + -5x + x2) 6 + -5x + x2 + (-4x2 + 2x + 7) = 0 Reorder the terms: 6 + -5x + x2 + (7 + 2x + -4x2) = 0 Remove parenthesis around (7 + 2x + -4x2) 6 + -5x + x2 + 7 + 2x + -4x2 = 0 Reorder the terms: 6 + 7 + -5x + 2x + x2 + -4x2 = 0 Combine like terms: 6 + 7 = 13 13 + -5x + 2x + x2 + -4x2 = 0 Combine like terms: -5x + 2x = -3x 13 + -3x + x2 + -4x2 = 0 Combine like terms: x2 + -4x2 = -3x2 13 + -3x + -3x2 = 0 Solving 13 + -3x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4.333333333 + x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + x + x2 = 0 + 4.333333333 x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 x + x2 = 4.333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 4.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 4.333333333 + 0.25 Combine like terms: 4.333333333 + 0.25 = 4.583333333 1.25 + x2 = 4.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.583333333 Calculate the square root of the right side: 2.140872096 Break this problem into two subproblems by setting (x + 0.5) equal to 2.140872096 and -2.140872096.Subproblem 1
x + 0.5 = 2.140872096 Simplifying x + 0.5 = 2.140872096 Reorder the terms: 0.5 + x = 2.140872096 Solving 0.5 + x = 2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.140872096 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.140872096 + -0.5 x = 2.140872096 + -0.5 Combine like terms: 2.140872096 + -0.5 = 1.640872096 x = 1.640872096 Simplifying x = 1.640872096Subproblem 2
x + 0.5 = -2.140872096 Simplifying x + 0.5 = -2.140872096 Reorder the terms: 0.5 + x = -2.140872096 Solving 0.5 + x = -2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.140872096 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.140872096 + -0.5 x = -2.140872096 + -0.5 Combine like terms: -2.140872096 + -0.5 = -2.640872096 x = -2.640872096 Simplifying x = -2.640872096Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640872096, -2.640872096}
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