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Simplifying 126x2 + -4x + -546 = 0 Reorder the terms: -546 + -4x + 126x2 = 0 Solving -546 + -4x + 126x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-273 + -2x + 63x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-273 + -2x + 63x2)' equal to zero and attempt to solve: Simplifying -273 + -2x + 63x2 = 0 Solving -273 + -2x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -4.333333333 + -0.03174603175x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -0.03174603175x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -0.03174603175x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -0.03174603175x + x2 = 0 + 4.333333333 -0.03174603175x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -0.03174603175x + x2 = 4.333333333 The x term is -0.03174603175x. Take half its coefficient (-0.01587301588). Square it (0.0002519526331) and add it to both sides. Add '0.0002519526331' to each side of the equation. -0.03174603175x + 0.0002519526331 + x2 = 4.333333333 + 0.0002519526331 Reorder the terms: 0.0002519526331 + -0.03174603175x + x2 = 4.333333333 + 0.0002519526331 Combine like terms: 4.333333333 + 0.0002519526331 = 4.3335852856331 0.0002519526331 + -0.03174603175x + x2 = 4.3335852856331 Factor a perfect square on the left side: (x + -0.01587301588)(x + -0.01587301588) = 4.3335852856331 Calculate the square root of the right side: 2.081726516 Break this problem into two subproblems by setting (x + -0.01587301588) equal to 2.081726516 and -2.081726516.Subproblem 1
x + -0.01587301588 = 2.081726516 Simplifying x + -0.01587301588 = 2.081726516 Reorder the terms: -0.01587301588 + x = 2.081726516 Solving -0.01587301588 + x = 2.081726516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01587301588' to each side of the equation. -0.01587301588 + 0.01587301588 + x = 2.081726516 + 0.01587301588 Combine like terms: -0.01587301588 + 0.01587301588 = 0.00000000000 0.00000000000 + x = 2.081726516 + 0.01587301588 x = 2.081726516 + 0.01587301588 Combine like terms: 2.081726516 + 0.01587301588 = 2.09759953188 x = 2.09759953188 Simplifying x = 2.09759953188Subproblem 2
x + -0.01587301588 = -2.081726516 Simplifying x + -0.01587301588 = -2.081726516 Reorder the terms: -0.01587301588 + x = -2.081726516 Solving -0.01587301588 + x = -2.081726516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01587301588' to each side of the equation. -0.01587301588 + 0.01587301588 + x = -2.081726516 + 0.01587301588 Combine like terms: -0.01587301588 + 0.01587301588 = 0.00000000000 0.00000000000 + x = -2.081726516 + 0.01587301588 x = -2.081726516 + 0.01587301588 Combine like terms: -2.081726516 + 0.01587301588 = -2.06585350012 x = -2.06585350012 Simplifying x = -2.06585350012Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.09759953188, -2.06585350012}Solution
x = {2.09759953188, -2.06585350012}
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