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Simplifying 4x2 + -16x + 4 = 10x + -1x2 + -16 Reorder the terms: 4 + -16x + 4x2 = 10x + -1x2 + -16 Reorder the terms: 4 + -16x + 4x2 = -16 + 10x + -1x2 Solving 4 + -16x + 4x2 = -16 + 10x + -1x2 Solving for variable 'x'. Reorder the terms: 4 + 16 + -16x + -10x + 4x2 + x2 = -16 + 10x + -1x2 + 16 + -10x + x2 Combine like terms: 4 + 16 = 20 20 + -16x + -10x + 4x2 + x2 = -16 + 10x + -1x2 + 16 + -10x + x2 Combine like terms: -16x + -10x = -26x 20 + -26x + 4x2 + x2 = -16 + 10x + -1x2 + 16 + -10x + x2 Combine like terms: 4x2 + x2 = 5x2 20 + -26x + 5x2 = -16 + 10x + -1x2 + 16 + -10x + x2 Reorder the terms: 20 + -26x + 5x2 = -16 + 16 + 10x + -10x + -1x2 + x2 Combine like terms: -16 + 16 = 0 20 + -26x + 5x2 = 0 + 10x + -10x + -1x2 + x2 20 + -26x + 5x2 = 10x + -10x + -1x2 + x2 Combine like terms: 10x + -10x = 0 20 + -26x + 5x2 = 0 + -1x2 + x2 20 + -26x + 5x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 20 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -5.2x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.2x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -5.2x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.2x + x2 = 0 + -4 -5.2x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.2x + x2 = -4 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -4 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -4 + 6.76 Combine like terms: -4 + 6.76 = 2.76 6.76 + -5.2x + x2 = 2.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (x + -2.6) equal to 1.661324773 and -1.661324773.Subproblem 1
x + -2.6 = 1.661324773 Simplifying x + -2.6 = 1.661324773 Reorder the terms: -2.6 + x = 1.661324773 Solving -2.6 + x = 1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 1.661324773 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 1.661324773 + 2.6 x = 1.661324773 + 2.6 Combine like terms: 1.661324773 + 2.6 = 4.261324773 x = 4.261324773 Simplifying x = 4.261324773Subproblem 2
x + -2.6 = -1.661324773 Simplifying x + -2.6 = -1.661324773 Reorder the terms: -2.6 + x = -1.661324773 Solving -2.6 + x = -1.661324773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -1.661324773 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -1.661324773 + 2.6 x = -1.661324773 + 2.6 Combine like terms: -1.661324773 + 2.6 = 0.938675227 x = 0.938675227 Simplifying x = 0.938675227Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.261324773, 0.938675227}
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