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Simplifying 4x(x + 38) = 2x + 47 Reorder the terms: 4x(38 + x) = 2x + 47 (38 * 4x + x * 4x) = 2x + 47 (152x + 4x2) = 2x + 47 Reorder the terms: 152x + 4x2 = 47 + 2x Solving 152x + 4x2 = 47 + 2x Solving for variable 'x'. Reorder the terms: -47 + 152x + -2x + 4x2 = 47 + 2x + -47 + -2x Combine like terms: 152x + -2x = 150x -47 + 150x + 4x2 = 47 + 2x + -47 + -2x Reorder the terms: -47 + 150x + 4x2 = 47 + -47 + 2x + -2x Combine like terms: 47 + -47 = 0 -47 + 150x + 4x2 = 0 + 2x + -2x -47 + 150x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -47 + 150x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.75 + 37.5x + x2 = 0 Move the constant term to the right: Add '11.75' to each side of the equation. -11.75 + 37.5x + 11.75 + x2 = 0 + 11.75 Reorder the terms: -11.75 + 11.75 + 37.5x + x2 = 0 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + 37.5x + x2 = 0 + 11.75 37.5x + x2 = 0 + 11.75 Combine like terms: 0 + 11.75 = 11.75 37.5x + x2 = 11.75 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 11.75 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 11.75 + 351.5625 Combine like terms: 11.75 + 351.5625 = 363.3125 351.5625 + 37.5x + x2 = 363.3125 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 363.3125 Calculate the square root of the right side: 19.060758117 Break this problem into two subproblems by setting (x + 18.75) equal to 19.060758117 and -19.060758117.Subproblem 1
x + 18.75 = 19.060758117 Simplifying x + 18.75 = 19.060758117 Reorder the terms: 18.75 + x = 19.060758117 Solving 18.75 + x = 19.060758117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 19.060758117 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 19.060758117 + -18.75 x = 19.060758117 + -18.75 Combine like terms: 19.060758117 + -18.75 = 0.310758117 x = 0.310758117 Simplifying x = 0.310758117Subproblem 2
x + 18.75 = -19.060758117 Simplifying x + 18.75 = -19.060758117 Reorder the terms: 18.75 + x = -19.060758117 Solving 18.75 + x = -19.060758117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -19.060758117 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -19.060758117 + -18.75 x = -19.060758117 + -18.75 Combine like terms: -19.060758117 + -18.75 = -37.810758117 x = -37.810758117 Simplifying x = -37.810758117Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.310758117, -37.810758117}
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