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Simplifying 4x * x = x + 3 * 7 Multiply x * x 4x2 = x + 3 * 7 Multiply 3 * 7 4x2 = x + 21 Reorder the terms: 4x2 = 21 + x Solving 4x2 = 21 + x Solving for variable 'x'. Reorder the terms: -21 + -1x + 4x2 = 21 + x + -21 + -1x Reorder the terms: -21 + -1x + 4x2 = 21 + -21 + x + -1x Combine like terms: 21 + -21 = 0 -21 + -1x + 4x2 = 0 + x + -1x -21 + -1x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -21 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -0.25x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -0.25x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -0.25x + x2 = 0 + 5.25 -0.25x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -0.25x + x2 = 5.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 5.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 5.25 + 0.015625 Combine like terms: 5.25 + 0.015625 = 5.265625 0.015625 + -0.25x + x2 = 5.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + -0.125) equal to 2.294694969 and -2.294694969.Subproblem 1
x + -0.125 = 2.294694969 Simplifying x + -0.125 = 2.294694969 Reorder the terms: -0.125 + x = 2.294694969 Solving -0.125 + x = 2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 2.294694969 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 2.294694969 + 0.125 x = 2.294694969 + 0.125 Combine like terms: 2.294694969 + 0.125 = 2.419694969 x = 2.419694969 Simplifying x = 2.419694969Subproblem 2
x + -0.125 = -2.294694969 Simplifying x + -0.125 = -2.294694969 Reorder the terms: -0.125 + x = -2.294694969 Solving -0.125 + x = -2.294694969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -2.294694969 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -2.294694969 + 0.125 x = -2.294694969 + 0.125 Combine like terms: -2.294694969 + 0.125 = -2.169694969 x = -2.169694969 Simplifying x = -2.169694969Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.419694969, -2.169694969}
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