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Simplifying 7X2 + 6X + -6 = 0 Reorder the terms: -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 = 0.5916326324 X = 0.5916326324 Simplifying X = 0.5916326324Subproblem 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 = -1.4487754896 X = -1.4487754896 Simplifying X = -1.4487754896Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.5916326324, -1.4487754896}
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