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Simplifying 4x2 = 5x + 2 Reorder the terms: 4x2 = 2 + 5x Solving 4x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -2 + -5x + 4x2 = 2 + 5x + -2 + -5x Reorder the terms: -2 + -5x + 4x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -2 + -5x + 4x2 = 0 + 5x + -5x -2 + -5x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.25x + x2 = 0 + 0.5 -1.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.25x + x2 = 0.5 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.5 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.5 + 0.390625 Combine like terms: 0.5 + 0.390625 = 0.890625 0.390625 + -1.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + -0.625) equal to 0.943729304 and -0.943729304.Subproblem 1
x + -0.625 = 0.943729304 Simplifying x + -0.625 = 0.943729304 Reorder the terms: -0.625 + x = 0.943729304 Solving -0.625 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.943729304 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.943729304 + 0.625 x = 0.943729304 + 0.625 Combine like terms: 0.943729304 + 0.625 = 1.568729304 x = 1.568729304 Simplifying x = 1.568729304Subproblem 2
x + -0.625 = -0.943729304 Simplifying x + -0.625 = -0.943729304 Reorder the terms: -0.625 + x = -0.943729304 Solving -0.625 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.943729304 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.943729304 + 0.625 x = -0.943729304 + 0.625 Combine like terms: -0.943729304 + 0.625 = -0.318729304 x = -0.318729304 Simplifying x = -0.318729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.568729304, -0.318729304}
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