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Simplifying x + 4x(x + 4) + -10 = 48 Reorder the terms: x + 4x(4 + x) + -10 = 48 x + (4 * 4x + x * 4x) + -10 = 48 x + (16x + 4x2) + -10 = 48 Reorder the terms: -10 + x + 16x + 4x2 = 48 Combine like terms: x + 16x = 17x -10 + 17x + 4x2 = 48 Solving -10 + 17x + 4x2 = 48 Solving for variable 'x'. Reorder the terms: -10 + -48 + 17x + 4x2 = 48 + -48 Combine like terms: -10 + -48 = -58 -58 + 17x + 4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -58 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -14.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 4.25x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 4.25x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 4.25x + x2 = 0 + 14.5 4.25x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 4.25x + x2 = 14.5 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 14.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 14.5 + 4.515625 Combine like terms: 14.5 + 4.515625 = 19.015625 4.515625 + 4.25x + x2 = 19.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 19.015625 Calculate the square root of the right side: 4.360690886 Break this problem into two subproblems by setting (x + 2.125) equal to 4.360690886 and -4.360690886.Subproblem 1
x + 2.125 = 4.360690886 Simplifying x + 2.125 = 4.360690886 Reorder the terms: 2.125 + x = 4.360690886 Solving 2.125 + x = 4.360690886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 4.360690886 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 4.360690886 + -2.125 x = 4.360690886 + -2.125 Combine like terms: 4.360690886 + -2.125 = 2.235690886 x = 2.235690886 Simplifying x = 2.235690886Subproblem 2
x + 2.125 = -4.360690886 Simplifying x + 2.125 = -4.360690886 Reorder the terms: 2.125 + x = -4.360690886 Solving 2.125 + x = -4.360690886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -4.360690886 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -4.360690886 + -2.125 x = -4.360690886 + -2.125 Combine like terms: -4.360690886 + -2.125 = -6.485690886 x = -6.485690886 Simplifying x = -6.485690886Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.235690886, -6.485690886}
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