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Simplifying (2x2 + 3x + -8) + (5x2 + -9x + 2) = 0 Reorder the terms: (-8 + 3x + 2x2) + (5x2 + -9x + 2) = 0 Remove parenthesis around (-8 + 3x + 2x2) -8 + 3x + 2x2 + (5x2 + -9x + 2) = 0 Reorder the terms: -8 + 3x + 2x2 + (2 + -9x + 5x2) = 0 Remove parenthesis around (2 + -9x + 5x2) -8 + 3x + 2x2 + 2 + -9x + 5x2 = 0 Reorder the terms: -8 + 2 + 3x + -9x + 2x2 + 5x2 = 0 Combine like terms: -8 + 2 = -6 -6 + 3x + -9x + 2x2 + 5x2 = 0 Combine like terms: 3x + -9x = -6x -6 + -6x + 2x2 + 5x2 = 0 Combine like terms: 2x2 + 5x2 = 7x2 -6 + -6x + 7x2 = 0 Solving -6 + -6x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -0.8571428571x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -0.8571428571x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -0.8571428571x + x2 = 0 + 0.8571428571 -0.8571428571x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -0.8571428571x + x2 = 0.8571428571 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 0.8571428571 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 0.8571428571 + 0.1836734694 Combine like terms: 0.8571428571 + 0.1836734694 = 1.0408163265 0.1836734694 + -0.8571428571x + x2 = 1.0408163265 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 1.0408163265 Calculate the square root of the right side: 1.020204061 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 1.020204061 and -1.020204061.Subproblem 1
x + -0.4285714286 = 1.020204061 Simplifying x + -0.4285714286 = 1.020204061 Reorder the terms: -0.4285714286 + x = 1.020204061 Solving -0.4285714286 + x = 1.020204061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.020204061 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.020204061 + 0.4285714286 x = 1.020204061 + 0.4285714286 Combine like terms: 1.020204061 + 0.4285714286 = 1.4487754896 x = 1.4487754896 Simplifying x = 1.4487754896Subproblem 2
x + -0.4285714286 = -1.020204061 Simplifying x + -0.4285714286 = -1.020204061 Reorder the terms: -0.4285714286 + x = -1.020204061 Solving -0.4285714286 + x = -1.020204061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.020204061 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.020204061 + 0.4285714286 x = -1.020204061 + 0.4285714286 Combine like terms: -1.020204061 + 0.4285714286 = -0.5916326324 x = -0.5916326324 Simplifying x = -0.5916326324Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4487754896, -0.5916326324}
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