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Simplifying (3x2 + 7x + -4) + (2x2 + -3x + -9) = 0 Reorder the terms: (-4 + 7x + 3x2) + (2x2 + -3x + -9) = 0 Remove parenthesis around (-4 + 7x + 3x2) -4 + 7x + 3x2 + (2x2 + -3x + -9) = 0 Reorder the terms: -4 + 7x + 3x2 + (-9 + -3x + 2x2) = 0 Remove parenthesis around (-9 + -3x + 2x2) -4 + 7x + 3x2 + -9 + -3x + 2x2 = 0 Reorder the terms: -4 + -9 + 7x + -3x + 3x2 + 2x2 = 0 Combine like terms: -4 + -9 = -13 -13 + 7x + -3x + 3x2 + 2x2 = 0 Combine like terms: 7x + -3x = 4x -13 + 4x + 3x2 + 2x2 = 0 Combine like terms: 3x2 + 2x2 = 5x2 -13 + 4x + 5x2 = 0 Solving -13 + 4x + 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'. -2.6 + 0.8x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 0.8x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 0.8x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 0.8x + x2 = 0 + 2.6 0.8x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 0.8x + x2 = 2.6 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 2.6 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 2.6 + 0.16 Combine like terms: 2.6 + 0.16 = 2.76 0.16 + 0.8x + x2 = 2.76 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (x + 0.4) equal to 1.661324773 and -1.661324773.Subproblem 1
x + 0.4 = 1.661324773 Simplifying x + 0.4 = 1.661324773 Reorder the terms: 0.4 + x = 1.661324773 Solving 0.4 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.661324773 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.661324773 + -0.4 x = 1.661324773 + -0.4 Combine like terms: 1.661324773 + -0.4 = 1.261324773 x = 1.261324773 Simplifying x = 1.261324773Subproblem 2
x + 0.4 = -1.661324773 Simplifying x + 0.4 = -1.661324773 Reorder the terms: 0.4 + x = -1.661324773 Solving 0.4 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.661324773 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.661324773 + -0.4 x = -1.661324773 + -0.4 Combine like terms: -1.661324773 + -0.4 = -2.061324773 x = -2.061324773 Simplifying x = -2.061324773Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.261324773, -2.061324773}
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