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Simplifying 4x2 + -32x + -25 = 0 Reorder the terms: -25 + -32x + 4x2 = 0 Solving -25 + -32x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -8x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -8x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -8x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -8x + x2 = 0 + 6.25 -8x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -8x + x2 = 6.25 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 = 6.25 + 16 Reorder the terms: 16 + -8x + x2 = 6.25 + 16 Combine like terms: 6.25 + 16 = 22.25 16 + -8x + x2 = 22.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -4) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -4 = 4.716990566 Simplifying x + -4 = 4.716990566 Reorder the terms: -4 + x = 4.716990566 Solving -4 + x = 4.716990566 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 = 4.716990566 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.716990566 + 4 x = 4.716990566 + 4 Combine like terms: 4.716990566 + 4 = 8.716990566 x = 8.716990566 Simplifying x = 8.716990566Subproblem 2
x + -4 = -4.716990566 Simplifying x + -4 = -4.716990566 Reorder the terms: -4 + x = -4.716990566 Solving -4 + x = -4.716990566 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 = -4.716990566 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.716990566 + 4 x = -4.716990566 + 4 Combine like terms: -4.716990566 + 4 = -0.716990566 x = -0.716990566 Simplifying x = -0.716990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.716990566, -0.716990566}
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