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Simplifying 49x2 + -42x + -441 = 0 Reorder the terms: -441 + -42x + 49x2 = 0 Solving -441 + -42x + 49x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(-63 + -6x + 7x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-63 + -6x + 7x2)' equal to zero and attempt to solve: Simplifying -63 + -6x + 7x2 = 0 Solving -63 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.8571428571x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.8571428571x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.8571428571x + x2 = 0 + 9 -0.8571428571x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.8571428571x + x2 = 9 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 = 9 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 9 + 0.1836734694 Combine like terms: 9 + 0.1836734694 = 9.1836734694 0.1836734694 + -0.8571428571x + x2 = 9.1836734694 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 9.1836734694 Calculate the square root of the right side: 3.030457634 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 3.030457634 and -3.030457634.Subproblem 1
x + -0.4285714286 = 3.030457634 Simplifying x + -0.4285714286 = 3.030457634 Reorder the terms: -0.4285714286 + x = 3.030457634 Solving -0.4285714286 + x = 3.030457634 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 = 3.030457634 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 3.030457634 + 0.4285714286 x = 3.030457634 + 0.4285714286 Combine like terms: 3.030457634 + 0.4285714286 = 3.4590290626 x = 3.4590290626 Simplifying x = 3.4590290626Subproblem 2
x + -0.4285714286 = -3.030457634 Simplifying x + -0.4285714286 = -3.030457634 Reorder the terms: -0.4285714286 + x = -3.030457634 Solving -0.4285714286 + x = -3.030457634 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 = -3.030457634 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -3.030457634 + 0.4285714286 x = -3.030457634 + 0.4285714286 Combine like terms: -3.030457634 + 0.4285714286 = -2.6018862054 x = -2.6018862054 Simplifying x = -2.6018862054Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4590290626, -2.6018862054}Solution
x = {3.4590290626, -2.6018862054}
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