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Simplifying 4x(x + 12) = 3x + 12 Reorder the terms: 4x(12 + x) = 3x + 12 (12 * 4x + x * 4x) = 3x + 12 (48x + 4x2) = 3x + 12 Reorder the terms: 48x + 4x2 = 12 + 3x Solving 48x + 4x2 = 12 + 3x Solving for variable 'x'. Reorder the terms: -12 + 48x + -3x + 4x2 = 12 + 3x + -12 + -3x Combine like terms: 48x + -3x = 45x -12 + 45x + 4x2 = 12 + 3x + -12 + -3x Reorder the terms: -12 + 45x + 4x2 = 12 + -12 + 3x + -3x Combine like terms: 12 + -12 = 0 -12 + 45x + 4x2 = 0 + 3x + -3x -12 + 45x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + 45x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 11.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 11.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 11.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 11.25x + x2 = 0 + 3 11.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 11.25x + x2 = 3 The x term is 11.25x. Take half its coefficient (5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. 11.25x + 31.640625 + x2 = 3 + 31.640625 Reorder the terms: 31.640625 + 11.25x + x2 = 3 + 31.640625 Combine like terms: 3 + 31.640625 = 34.640625 31.640625 + 11.25x + x2 = 34.640625 Factor a perfect square on the left side: (x + 5.625)(x + 5.625) = 34.640625 Calculate the square root of the right side: 5.885628683 Break this problem into two subproblems by setting (x + 5.625) equal to 5.885628683 and -5.885628683.Subproblem 1
x + 5.625 = 5.885628683 Simplifying x + 5.625 = 5.885628683 Reorder the terms: 5.625 + x = 5.885628683 Solving 5.625 + x = 5.885628683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = 5.885628683 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = 5.885628683 + -5.625 x = 5.885628683 + -5.625 Combine like terms: 5.885628683 + -5.625 = 0.260628683 x = 0.260628683 Simplifying x = 0.260628683Subproblem 2
x + 5.625 = -5.885628683 Simplifying x + 5.625 = -5.885628683 Reorder the terms: 5.625 + x = -5.885628683 Solving 5.625 + x = -5.885628683 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.625' to each side of the equation. 5.625 + -5.625 + x = -5.885628683 + -5.625 Combine like terms: 5.625 + -5.625 = 0.000 0.000 + x = -5.885628683 + -5.625 x = -5.885628683 + -5.625 Combine like terms: -5.885628683 + -5.625 = -11.510628683 x = -11.510628683 Simplifying x = -11.510628683Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.260628683, -11.510628683}
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