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Simplifying 4x = 2x2 + 20x + -33 Reorder the terms: 4x = -33 + 20x + 2x2 Solving 4x = -33 + 20x + 2x2 Solving for variable 'x'. Reorder the terms: 33 + 4x + -20x + -2x2 = -33 + 20x + 2x2 + 33 + -20x + -2x2 Combine like terms: 4x + -20x = -16x 33 + -16x + -2x2 = -33 + 20x + 2x2 + 33 + -20x + -2x2 Reorder the terms: 33 + -16x + -2x2 = -33 + 33 + 20x + -20x + 2x2 + -2x2 Combine like terms: -33 + 33 = 0 33 + -16x + -2x2 = 0 + 20x + -20x + 2x2 + -2x2 33 + -16x + -2x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 33 + -16x + -2x2 = 0 + 2x2 + -2x2 33 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 33 + -16x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -16.5 + 8x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 8x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 8x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 8x + x2 = 0 + 16.5 8x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 8x + x2 = 16.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 16.5 + 16 Reorder the terms: 16 + 8x + x2 = 16.5 + 16 Combine like terms: 16.5 + 16 = 32.5 16 + 8x + x2 = 32.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (x + 4) equal to 5.700877125 and -5.700877125.Subproblem 1
x + 4 = 5.700877125 Simplifying x + 4 = 5.700877125 Reorder the terms: 4 + x = 5.700877125 Solving 4 + x = 5.700877125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.700877125 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.700877125 + -4 x = 5.700877125 + -4 Combine like terms: 5.700877125 + -4 = 1.700877125 x = 1.700877125 Simplifying x = 1.700877125Subproblem 2
x + 4 = -5.700877125 Simplifying x + 4 = -5.700877125 Reorder the terms: 4 + x = -5.700877125 Solving 4 + x = -5.700877125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.700877125 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.700877125 + -4 x = -5.700877125 + -4 Combine like terms: -5.700877125 + -4 = -9.700877125 x = -9.700877125 Simplifying x = -9.700877125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.700877125, -9.700877125}
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