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Simplifying 4x2 + 2x = -4x + 21 Reorder the terms: 2x + 4x2 = -4x + 21 Reorder the terms: 2x + 4x2 = 21 + -4x Solving 2x + 4x2 = 21 + -4x Solving for variable 'x'. Reorder the terms: -21 + 2x + 4x + 4x2 = 21 + -4x + -21 + 4x Combine like terms: 2x + 4x = 6x -21 + 6x + 4x2 = 21 + -4x + -21 + 4x Reorder the terms: -21 + 6x + 4x2 = 21 + -21 + -4x + 4x Combine like terms: 21 + -21 = 0 -21 + 6x + 4x2 = 0 + -4x + 4x -21 + 6x + 4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -21 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 1.5x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 1.5x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 1.5x + x2 = 0 + 5.25 1.5x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 1.5x + x2 = 5.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.25 + 0.5625 Combine like terms: 5.25 + 0.5625 = 5.8125 0.5625 + 1.5x + x2 = 5.8125 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 5.8125 Calculate the square root of the right side: 2.41091269 Break this problem into two subproblems by setting (x + 0.75) equal to 2.41091269 and -2.41091269.Subproblem 1
x + 0.75 = 2.41091269 Simplifying x + 0.75 = 2.41091269 Reorder the terms: 0.75 + x = 2.41091269 Solving 0.75 + x = 2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.41091269 + -0.75 x = 2.41091269 + -0.75 Combine like terms: 2.41091269 + -0.75 = 1.66091269 x = 1.66091269 Simplifying x = 1.66091269Subproblem 2
x + 0.75 = -2.41091269 Simplifying x + 0.75 = -2.41091269 Reorder the terms: 0.75 + x = -2.41091269 Solving 0.75 + x = -2.41091269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.41091269 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.41091269 + -0.75 x = -2.41091269 + -0.75 Combine like terms: -2.41091269 + -0.75 = -3.16091269 x = -3.16091269 Simplifying x = -3.16091269Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.66091269, -3.16091269}
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