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Simplifying (2x2 + 3x + -4) + -1(4x2 + -7x + 1) = 0 Reorder the terms: (-4 + 3x + 2x2) + -1(4x2 + -7x + 1) = 0 Remove parenthesis around (-4 + 3x + 2x2) -4 + 3x + 2x2 + -1(4x2 + -7x + 1) = 0 Reorder the terms: -4 + 3x + 2x2 + -1(1 + -7x + 4x2) = 0 -4 + 3x + 2x2 + (1 * -1 + -7x * -1 + 4x2 * -1) = 0 -4 + 3x + 2x2 + (-1 + 7x + -4x2) = 0 Reorder the terms: -4 + -1 + 3x + 7x + 2x2 + -4x2 = 0 Combine like terms: -4 + -1 = -5 -5 + 3x + 7x + 2x2 + -4x2 = 0 Combine like terms: 3x + 7x = 10x -5 + 10x + 2x2 + -4x2 = 0 Combine like terms: 2x2 + -4x2 = -2x2 -5 + 10x + -2x2 = 0 Solving -5 + 10x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5x + x2 = 0 + -2.5 -5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5x + x2 = -2.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -2.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.5 + 6.25 Combine like terms: -2.5 + 6.25 = 3.75 6.25 + -5x + x2 = 3.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (x + -2.5) equal to 1.936491673 and -1.936491673.Subproblem 1
x + -2.5 = 1.936491673 Simplifying x + -2.5 = 1.936491673 Reorder the terms: -2.5 + x = 1.936491673 Solving -2.5 + x = 1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.936491673 + 2.5 x = 1.936491673 + 2.5 Combine like terms: 1.936491673 + 2.5 = 4.436491673 x = 4.436491673 Simplifying x = 4.436491673Subproblem 2
x + -2.5 = -1.936491673 Simplifying x + -2.5 = -1.936491673 Reorder the terms: -2.5 + x = -1.936491673 Solving -2.5 + x = -1.936491673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.936491673 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.936491673 + 2.5 x = -1.936491673 + 2.5 Combine like terms: -1.936491673 + 2.5 = 0.563508327 x = 0.563508327 Simplifying x = 0.563508327Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.436491673, 0.563508327}
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