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Simplifying 63x2 + -11x + -3 = 0 Reorder the terms: -3 + -11x + 63x2 = 0 Solving -3 + -11x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.04761904762 + -0.1746031746x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + -0.1746031746x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + -0.1746031746x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + -0.1746031746x + x2 = 0 + 0.04761904762 -0.1746031746x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 -0.1746031746x + x2 = 0.04761904762 The x term is -0.1746031746x. Take half its coefficient (-0.0873015873). Square it (0.007621567145) and add it to both sides. Add '0.007621567145' to each side of the equation. -0.1746031746x + 0.007621567145 + x2 = 0.04761904762 + 0.007621567145 Reorder the terms: 0.007621567145 + -0.1746031746x + x2 = 0.04761904762 + 0.007621567145 Combine like terms: 0.04761904762 + 0.007621567145 = 0.055240614765 0.007621567145 + -0.1746031746x + x2 = 0.055240614765 Factor a perfect square on the left side: (x + -0.0873015873)(x + -0.0873015873) = 0.055240614765 Calculate the square root of the right side: 0.235033221 Break this problem into two subproblems by setting (x + -0.0873015873) equal to 0.235033221 and -0.235033221.Subproblem 1
x + -0.0873015873 = 0.235033221 Simplifying x + -0.0873015873 = 0.235033221 Reorder the terms: -0.0873015873 + x = 0.235033221 Solving -0.0873015873 + x = 0.235033221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0873015873' to each side of the equation. -0.0873015873 + 0.0873015873 + x = 0.235033221 + 0.0873015873 Combine like terms: -0.0873015873 + 0.0873015873 = 0.0000000000 0.0000000000 + x = 0.235033221 + 0.0873015873 x = 0.235033221 + 0.0873015873 Combine like terms: 0.235033221 + 0.0873015873 = 0.3223348083 x = 0.3223348083 Simplifying x = 0.3223348083Subproblem 2
x + -0.0873015873 = -0.235033221 Simplifying x + -0.0873015873 = -0.235033221 Reorder the terms: -0.0873015873 + x = -0.235033221 Solving -0.0873015873 + x = -0.235033221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0873015873' to each side of the equation. -0.0873015873 + 0.0873015873 + x = -0.235033221 + 0.0873015873 Combine like terms: -0.0873015873 + 0.0873015873 = 0.0000000000 0.0000000000 + x = -0.235033221 + 0.0873015873 x = -0.235033221 + 0.0873015873 Combine like terms: -0.235033221 + 0.0873015873 = -0.1477316337 x = -0.1477316337 Simplifying x = -0.1477316337Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3223348083, -0.1477316337}
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