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Simplifying (4x2 + -3x + 7) + (2x2 + 6x + -8) = 0 Reorder the terms: (7 + -3x + 4x2) + (2x2 + 6x + -8) = 0 Remove parenthesis around (7 + -3x + 4x2) 7 + -3x + 4x2 + (2x2 + 6x + -8) = 0 Reorder the terms: 7 + -3x + 4x2 + (-8 + 6x + 2x2) = 0 Remove parenthesis around (-8 + 6x + 2x2) 7 + -3x + 4x2 + -8 + 6x + 2x2 = 0 Reorder the terms: 7 + -8 + -3x + 6x + 4x2 + 2x2 = 0 Combine like terms: 7 + -8 = -1 -1 + -3x + 6x + 4x2 + 2x2 = 0 Combine like terms: -3x + 6x = 3x -1 + 3x + 4x2 + 2x2 = 0 Combine like terms: 4x2 + 2x2 = 6x2 -1 + 3x + 6x2 = 0 Solving -1 + 3x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.1666666667 0.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.5x + x2 = 0.1666666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.1666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.1666666667 + 0.0625 Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667 0.0625 + 0.5x + x2 = 0.2291666667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2291666667 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + 0.25) equal to 0.478713554 and -0.478713554.Subproblem 1
x + 0.25 = 0.478713554 Simplifying x + 0.25 = 0.478713554 Reorder the terms: 0.25 + x = 0.478713554 Solving 0.25 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.478713554 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.478713554 + -0.25 x = 0.478713554 + -0.25 Combine like terms: 0.478713554 + -0.25 = 0.228713554 x = 0.228713554 Simplifying x = 0.228713554Subproblem 2
x + 0.25 = -0.478713554 Simplifying x + 0.25 = -0.478713554 Reorder the terms: 0.25 + x = -0.478713554 Solving 0.25 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.478713554 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.478713554 + -0.25 x = -0.478713554 + -0.25 Combine like terms: -0.478713554 + -0.25 = -0.728713554 x = -0.728713554 Simplifying x = -0.728713554Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.228713554, -0.728713554}
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