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Simplifying 49x2 + -15 = 4x Reorder the terms: -15 + 49x2 = 4x Solving -15 + 49x2 = 4x Solving for variable 'x'. Reorder the terms: -15 + -4x + 49x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -15 + -4x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.306122449 + -0.08163265306x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -0.08163265306x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -0.08163265306x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -0.08163265306x + x2 = 0 + 0.306122449 -0.08163265306x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -0.08163265306x + x2 = 0.306122449 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 = 0.306122449 + 0.001665972511 Reorder the terms: 0.001665972511 + -0.08163265306x + x2 = 0.306122449 + 0.001665972511 Combine like terms: 0.306122449 + 0.001665972511 = 0.307788421511 0.001665972511 + -0.08163265306x + x2 = 0.307788421511 Factor a perfect square on the left side: (x + -0.04081632653)(x + -0.04081632653) = 0.307788421511 Calculate the square root of the right side: 0.554786825 Break this problem into two subproblems by setting (x + -0.04081632653) equal to 0.554786825 and -0.554786825.Subproblem 1
x + -0.04081632653 = 0.554786825 Simplifying x + -0.04081632653 = 0.554786825 Reorder the terms: -0.04081632653 + x = 0.554786825 Solving -0.04081632653 + x = 0.554786825 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 = 0.554786825 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + x = 0.554786825 + 0.04081632653 x = 0.554786825 + 0.04081632653 Combine like terms: 0.554786825 + 0.04081632653 = 0.59560315153 x = 0.59560315153 Simplifying x = 0.59560315153Subproblem 2
x + -0.04081632653 = -0.554786825 Simplifying x + -0.04081632653 = -0.554786825 Reorder the terms: -0.04081632653 + x = -0.554786825 Solving -0.04081632653 + x = -0.554786825 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 = -0.554786825 + 0.04081632653 Combine like terms: -0.04081632653 + 0.04081632653 = 0.00000000000 0.00000000000 + x = -0.554786825 + 0.04081632653 x = -0.554786825 + 0.04081632653 Combine like terms: -0.554786825 + 0.04081632653 = -0.51397049847 x = -0.51397049847 Simplifying x = -0.51397049847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.59560315153, -0.51397049847}
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