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Simplifying (7x2 + -4x + 1) + (3x2 + -9x + -5) = 0 Reorder the terms: (1 + -4x + 7x2) + (3x2 + -9x + -5) = 0 Remove parenthesis around (1 + -4x + 7x2) 1 + -4x + 7x2 + (3x2 + -9x + -5) = 0 Reorder the terms: 1 + -4x + 7x2 + (-5 + -9x + 3x2) = 0 Remove parenthesis around (-5 + -9x + 3x2) 1 + -4x + 7x2 + -5 + -9x + 3x2 = 0 Reorder the terms: 1 + -5 + -4x + -9x + 7x2 + 3x2 = 0 Combine like terms: 1 + -5 = -4 -4 + -4x + -9x + 7x2 + 3x2 = 0 Combine like terms: -4x + -9x = -13x -4 + -13x + 7x2 + 3x2 = 0 Combine like terms: 7x2 + 3x2 = 10x2 -4 + -13x + 10x2 = 0 Solving -4 + -13x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.4 + -1.3x + x2 = 0.0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -1.3x + 0.4 + x2 = 0.0 + 0.4 Reorder the terms: -0.4 + 0.4 + -1.3x + x2 = 0.0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -1.3x + x2 = 0.0 + 0.4 -1.3x + x2 = 0.0 + 0.4 Combine like terms: 0.0 + 0.4 = 0.4 -1.3x + x2 = 0.4 The x term is -1.3x. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x + 0.4225 + x2 = 0.4 + 0.4225 Reorder the terms: 0.4225 + -1.3x + x2 = 0.4 + 0.4225 Combine like terms: 0.4 + 0.4225 = 0.8225 0.4225 + -1.3x + x2 = 0.8225 Factor a perfect square on the left side: (x + -0.65)(x + -0.65) = 0.8225 Calculate the square root of the right side: 0.906917857 Break this problem into two subproblems by setting (x + -0.65) equal to 0.906917857 and -0.906917857.Subproblem 1
x + -0.65 = 0.906917857 Simplifying x + -0.65 = 0.906917857 Reorder the terms: -0.65 + x = 0.906917857 Solving -0.65 + x = 0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = 0.906917857 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = 0.906917857 + 0.65 x = 0.906917857 + 0.65 Combine like terms: 0.906917857 + 0.65 = 1.556917857 x = 1.556917857 Simplifying x = 1.556917857Subproblem 2
x + -0.65 = -0.906917857 Simplifying x + -0.65 = -0.906917857 Reorder the terms: -0.65 + x = -0.906917857 Solving -0.65 + x = -0.906917857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x = -0.906917857 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x = -0.906917857 + 0.65 x = -0.906917857 + 0.65 Combine like terms: -0.906917857 + 0.65 = -0.256917857 x = -0.256917857 Simplifying x = -0.256917857Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.556917857, -0.256917857}
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