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Simplifying x + 50 = (x + 10) * 4x Reorder the terms: 50 + x = (x + 10) * 4x Reorder the terms: 50 + x = (10 + x) * 4x Reorder the terms for easier multiplication: 50 + x = 4x(10 + x) 50 + x = (10 * 4x + x * 4x) 50 + x = (40x + 4x2) Solving 50 + x = 40x + 4x2 Solving for variable 'x'. Combine like terms: x + -40x = -39x 50 + -39x + -4x2 = 40x + 4x2 + -40x + -4x2 Reorder the terms: 50 + -39x + -4x2 = 40x + -40x + 4x2 + -4x2 Combine like terms: 40x + -40x = 0 50 + -39x + -4x2 = 0 + 4x2 + -4x2 50 + -39x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 50 + -39x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -12.5 + 9.75x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 9.75x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 9.75x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 9.75x + x2 = 0 + 12.5 9.75x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 9.75x + x2 = 12.5 The x term is 9.75x. Take half its coefficient (4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. 9.75x + 23.765625 + x2 = 12.5 + 23.765625 Reorder the terms: 23.765625 + 9.75x + x2 = 12.5 + 23.765625 Combine like terms: 12.5 + 23.765625 = 36.265625 23.765625 + 9.75x + x2 = 36.265625 Factor a perfect square on the left side: (x + 4.875)(x + 4.875) = 36.265625 Calculate the square root of the right side: 6.022094735 Break this problem into two subproblems by setting (x + 4.875) equal to 6.022094735 and -6.022094735.Subproblem 1
x + 4.875 = 6.022094735 Simplifying x + 4.875 = 6.022094735 Reorder the terms: 4.875 + x = 6.022094735 Solving 4.875 + x = 6.022094735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = 6.022094735 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = 6.022094735 + -4.875 x = 6.022094735 + -4.875 Combine like terms: 6.022094735 + -4.875 = 1.147094735 x = 1.147094735 Simplifying x = 1.147094735Subproblem 2
x + 4.875 = -6.022094735 Simplifying x + 4.875 = -6.022094735 Reorder the terms: 4.875 + x = -6.022094735 Solving 4.875 + x = -6.022094735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.875' to each side of the equation. 4.875 + -4.875 + x = -6.022094735 + -4.875 Combine like terms: 4.875 + -4.875 = 0.000 0.000 + x = -6.022094735 + -4.875 x = -6.022094735 + -4.875 Combine like terms: -6.022094735 + -4.875 = -10.897094735 x = -10.897094735 Simplifying x = -10.897094735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.147094735, -10.897094735}
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