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Simplifying 0.2(x + 50) + -6 = 0.4x(3x + 20) Reorder the terms: 0.2(50 + x) + -6 = 0.4x(3x + 20) (50 * 0.2 + x * 0.2) + -6 = 0.4x(3x + 20) (10 + 0.2x) + -6 = 0.4x(3x + 20) Reorder the terms: 10 + -6 + 0.2x = 0.4x(3x + 20) Combine like terms: 10 + -6 = 4 4 + 0.2x = 0.4x(3x + 20) Reorder the terms: 4 + 0.2x = 0.4x(20 + 3x) 4 + 0.2x = (20 * 0.4x + 3x * 0.4x) 4 + 0.2x = (8x + 1.2x2) Solving 4 + 0.2x = 8x + 1.2x2 Solving for variable 'x'. Combine like terms: 0.2x + -8x = -7.8x 4 + -7.8x + -1.2x2 = 8x + 1.2x2 + -8x + -1.2x2 Reorder the terms: 4 + -7.8x + -1.2x2 = 8x + -8x + 1.2x2 + -1.2x2 Combine like terms: 8x + -8x = 0 4 + -7.8x + -1.2x2 = 0 + 1.2x2 + -1.2x2 4 + -7.8x + -1.2x2 = 1.2x2 + -1.2x2 Combine like terms: 1.2x2 + -1.2x2 = 0.0 4 + -7.8x + -1.2x2 = 0.0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -3.333333333 + 6.5x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 6.5x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 6.5x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 6.5x + x2 = 0 + 3.333333333 6.5x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 6.5x + x2 = 3.333333333 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 3.333333333 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 3.333333333 + 10.5625 Combine like terms: 3.333333333 + 10.5625 = 13.895833333 10.5625 + 6.5x + x2 = 13.895833333 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 13.895833333 Calculate the square root of the right side: 3.727711541 Break this problem into two subproblems by setting (x + 3.25) equal to 3.727711541 and -3.727711541.Subproblem 1
x + 3.25 = 3.727711541 Simplifying x + 3.25 = 3.727711541 Reorder the terms: 3.25 + x = 3.727711541 Solving 3.25 + x = 3.727711541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.727711541 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.727711541 + -3.25 x = 3.727711541 + -3.25 Combine like terms: 3.727711541 + -3.25 = 0.477711541 x = 0.477711541 Simplifying x = 0.477711541Subproblem 2
x + 3.25 = -3.727711541 Simplifying x + 3.25 = -3.727711541 Reorder the terms: 3.25 + x = -3.727711541 Solving 3.25 + x = -3.727711541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.727711541 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.727711541 + -3.25 x = -3.727711541 + -3.25 Combine like terms: -3.727711541 + -3.25 = -6.977711541 x = -6.977711541 Simplifying x = -6.977711541Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.477711541, -6.977711541}
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