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Simplifying (3x2 + 4x + -1) + (x2 + 3x + -5) = 0 Reorder the terms: (-1 + 4x + 3x2) + (x2 + 3x + -5) = 0 Remove parenthesis around (-1 + 4x + 3x2) -1 + 4x + 3x2 + (x2 + 3x + -5) = 0 Reorder the terms: -1 + 4x + 3x2 + (-5 + 3x + x2) = 0 Remove parenthesis around (-5 + 3x + x2) -1 + 4x + 3x2 + -5 + 3x + x2 = 0 Reorder the terms: -1 + -5 + 4x + 3x + 3x2 + x2 = 0 Combine like terms: -1 + -5 = -6 -6 + 4x + 3x + 3x2 + x2 = 0 Combine like terms: 4x + 3x = 7x -6 + 7x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 -6 + 7x + 4x2 = 0 Solving -6 + 7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.75x + x2 = 0 + 1.5 1.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.75x + x2 = 1.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1.5 + 0.765625 Combine like terms: 1.5 + 0.765625 = 2.265625 0.765625 + 1.75x + x2 = 2.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (x + 0.875) equal to 1.505199322 and -1.505199322.Subproblem 1
x + 0.875 = 1.505199322 Simplifying x + 0.875 = 1.505199322 Reorder the terms: 0.875 + x = 1.505199322 Solving 0.875 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.505199322 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.505199322 + -0.875 x = 1.505199322 + -0.875 Combine like terms: 1.505199322 + -0.875 = 0.630199322 x = 0.630199322 Simplifying x = 0.630199322Subproblem 2
x + 0.875 = -1.505199322 Simplifying x + 0.875 = -1.505199322 Reorder the terms: 0.875 + x = -1.505199322 Solving 0.875 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.505199322 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.505199322 + -0.875 x = -1.505199322 + -0.875 Combine like terms: -1.505199322 + -0.875 = -2.380199322 x = -2.380199322 Simplifying x = -2.380199322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.630199322, -2.380199322}
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