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Simplifying 4x2 = 32x + 45 Reorder the terms: 4x2 = 45 + 32x Solving 4x2 = 45 + 32x Solving for variable 'x'. Reorder the terms: -45 + -32x + 4x2 = 45 + 32x + -45 + -32x Reorder the terms: -45 + -32x + 4x2 = 45 + -45 + 32x + -32x Combine like terms: 45 + -45 = 0 -45 + -32x + 4x2 = 0 + 32x + -32x -45 + -32x + 4x2 = 32x + -32x Combine like terms: 32x + -32x = 0 -45 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -8x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -8x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -8x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -8x + x2 = 0 + 11.25 -8x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -8x + x2 = 11.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 11.25 + 16 Reorder the terms: 16 + -8x + x2 = 11.25 + 16 Combine like terms: 11.25 + 16 = 27.25 16 + -8x + x2 = 27.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + -4) equal to 5.220153254 and -5.220153254.Subproblem 1
x + -4 = 5.220153254 Simplifying x + -4 = 5.220153254 Reorder the terms: -4 + x = 5.220153254 Solving -4 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.220153254 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.220153254 + 4 x = 5.220153254 + 4 Combine like terms: 5.220153254 + 4 = 9.220153254 x = 9.220153254 Simplifying x = 9.220153254Subproblem 2
x + -4 = -5.220153254 Simplifying x + -4 = -5.220153254 Reorder the terms: -4 + x = -5.220153254 Solving -4 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.220153254 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.220153254 + 4 x = -5.220153254 + 4 Combine like terms: -5.220153254 + 4 = -1.220153254 x = -1.220153254 Simplifying x = -1.220153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.220153254, -1.220153254}
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