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Simplifying (7x2 + 8x + -6) + (3x2 + -9x + 5) = 0 Reorder the terms: (-6 + 8x + 7x2) + (3x2 + -9x + 5) = 0 Remove parenthesis around (-6 + 8x + 7x2) -6 + 8x + 7x2 + (3x2 + -9x + 5) = 0 Reorder the terms: -6 + 8x + 7x2 + (5 + -9x + 3x2) = 0 Remove parenthesis around (5 + -9x + 3x2) -6 + 8x + 7x2 + 5 + -9x + 3x2 = 0 Reorder the terms: -6 + 5 + 8x + -9x + 7x2 + 3x2 = 0 Combine like terms: -6 + 5 = -1 -1 + 8x + -9x + 7x2 + 3x2 = 0 Combine like terms: 8x + -9x = -1x -1 + -1x + 7x2 + 3x2 = 0 Combine like terms: 7x2 + 3x2 = 10x2 -1 + -1x + 10x2 = 0 Solving -1 + -1x + 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'. -0.1 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.1x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.1x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.1x + x2 = 0.0 + 0.1 -0.1x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -0.1x + x2 = 0.1 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = 0.1 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.1 + 0.0025 Combine like terms: 0.1 + 0.0025 = 0.1025 0.0025 + -0.1x + x2 = 0.1025 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.1025 Calculate the square root of the right side: 0.320156212 Break this problem into two subproblems by setting (x + -0.05) equal to 0.320156212 and -0.320156212.Subproblem 1
x + -0.05 = 0.320156212 Simplifying x + -0.05 = 0.320156212 Reorder the terms: -0.05 + x = 0.320156212 Solving -0.05 + x = 0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = 0.320156212 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.320156212 + 0.05 x = 0.320156212 + 0.05 Combine like terms: 0.320156212 + 0.05 = 0.370156212 x = 0.370156212 Simplifying x = 0.370156212Subproblem 2
x + -0.05 = -0.320156212 Simplifying x + -0.05 = -0.320156212 Reorder the terms: -0.05 + x = -0.320156212 Solving -0.05 + x = -0.320156212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05' to each side of the equation. -0.05 + 0.05 + x = -0.320156212 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.320156212 + 0.05 x = -0.320156212 + 0.05 Combine like terms: -0.320156212 + 0.05 = -0.270156212 x = -0.270156212 Simplifying x = -0.270156212Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.370156212, -0.270156212}
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