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Simplifying 0.5x2 + 2(3x) + 2(x + 2) = 336 Remove parenthesis around (3x) 0.5x2 + 2 * 3x + 2(x + 2) = 336 Multiply 2 * 3 0.5x2 + 6x + 2(x + 2) = 336 Reorder the terms: 0.5x2 + 6x + 2(2 + x) = 336 0.5x2 + 6x + (2 * 2 + x * 2) = 336 0.5x2 + 6x + (4 + 2x) = 336 Reorder the terms: 4 + 6x + 2x + 0.5x2 = 336 Combine like terms: 6x + 2x = 8x 4 + 8x + 0.5x2 = 336 Solving 4 + 8x + 0.5x2 = 336 Solving for variable 'x'. Reorder the terms: 4 + -336 + 8x + 0.5x2 = 336 + -336 Combine like terms: 4 + -336 = -332 -332 + 8x + 0.5x2 = 336 + -336 Combine like terms: 336 + -336 = 0 -332 + 8x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -664 + 16x + x2 = 0 Move the constant term to the right: Add '664' to each side of the equation. -664 + 16x + 664 + x2 = 0 + 664 Reorder the terms: -664 + 664 + 16x + x2 = 0 + 664 Combine like terms: -664 + 664 = 0 0 + 16x + x2 = 0 + 664 16x + x2 = 0 + 664 Combine like terms: 0 + 664 = 664 16x + x2 = 664 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 664 + 64 Reorder the terms: 64 + 16x + x2 = 664 + 64 Combine like terms: 664 + 64 = 728 64 + 16x + x2 = 728 Factor a perfect square on the left side: (x + 8)(x + 8) = 728 Calculate the square root of the right side: 26.981475126 Break this problem into two subproblems by setting (x + 8) equal to 26.981475126 and -26.981475126.Subproblem 1
x + 8 = 26.981475126 Simplifying x + 8 = 26.981475126 Reorder the terms: 8 + x = 26.981475126 Solving 8 + x = 26.981475126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 26.981475126 + -8 Combine like terms: 8 + -8 = 0 0 + x = 26.981475126 + -8 x = 26.981475126 + -8 Combine like terms: 26.981475126 + -8 = 18.981475126 x = 18.981475126 Simplifying x = 18.981475126Subproblem 2
x + 8 = -26.981475126 Simplifying x + 8 = -26.981475126 Reorder the terms: 8 + x = -26.981475126 Solving 8 + x = -26.981475126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -26.981475126 + -8 Combine like terms: 8 + -8 = 0 0 + x = -26.981475126 + -8 x = -26.981475126 + -8 Combine like terms: -26.981475126 + -8 = -34.981475126 x = -34.981475126 Simplifying x = -34.981475126Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.981475126, -34.981475126}
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