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Simplifying -54 + -4x + 49x2 = 0 Solving -54 + -4x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.102040816 + -0.08163265306x + x2 = 0 Move the constant term to the right: Add '1.102040816' to each side of the equation. -1.102040816 + -0.08163265306x + 1.102040816 + x2 = 0 + 1.102040816 Reorder the terms: -1.102040816 + 1.102040816 + -0.08163265306x + x2 = 0 + 1.102040816 Combine like terms: -1.102040816 + 1.102040816 = 0.000000000 0.000000000 + -0.08163265306x + x2 = 0 + 1.102040816 -0.08163265306x + x2 = 0 + 1.102040816 Combine like terms: 0 + 1.102040816 = 1.102040816 -0.08163265306x + x2 = 1.102040816 The x term is -0.08163265306x. Take half its coefficient (-0.04081632653). Square it (0.001665972511) and add it to both sides. Add '0.001665972511' to each side of the equation. -0.08163265306x + 0.001665972511 + x2 = 1.102040816 + 0.001665972511 Reorder the terms: 0.001665972511 + -0.08163265306x + x2 = 1.102040816 + 0.001665972511 Combine like terms: 1.102040816 + 0.001665972511 = 1.103706788511 0.001665972511 + -0.08163265306x + x2 = 1.103706788511 Factor a perfect square on the left side: (x + -0.04081632653)(x + -0.04081632653) = 1.103706788511 Calculate the square root of the right side: 1.050574504 Break this problem into two subproblems by setting (x + -0.04081632653) equal to 1.050574504 and -1.050574504.Subproblem 1
x + -0.04081632653 = 1.050574504 Simplifying x + -0.04081632653 = 1.050574504 Reorder the terms: -0.04081632653 + x = 1.050574504 Solving -0.04081632653 + x = 1.050574504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04081632653' to each side of the equation. -0.04081632653 + 0.04081632653 + x = 1.050574504 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + x = 1.050574504 + 0.04081632653 x = 1.050574504 + 0.04081632653 Combine like terms: 1.050574504 + 0.04081632653 = 1.09139083053 x = 1.09139083053 Simplifying x = 1.09139083053Subproblem 2
x + -0.04081632653 = -1.050574504 Simplifying x + -0.04081632653 = -1.050574504 Reorder the terms: -0.04081632653 + x = -1.050574504 Solving -0.04081632653 + x = -1.050574504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04081632653' to each side of the equation. -0.04081632653 + 0.04081632653 + x = -1.050574504 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + x = -1.050574504 + 0.04081632653 x = -1.050574504 + 0.04081632653 Combine like terms: -1.050574504 + 0.04081632653 = -1.00975817747 x = -1.00975817747 Simplifying x = -1.00975817747Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.09139083053, -1.00975817747}
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