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Simplifying 4x2 + -13x + -25 = 4 Reorder the terms: -25 + -13x + 4x2 = 4 Solving -25 + -13x + 4x2 = 4 Solving for variable 'x'. Reorder the terms: -25 + -4 + -13x + 4x2 = 4 + -4 Combine like terms: -25 + -4 = -29 -29 + -13x + 4x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -29 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -3.25x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -3.25x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -3.25x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -3.25x + x2 = 0 + 7.25 -3.25x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -3.25x + x2 = 7.25 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 7.25 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 7.25 + 2.640625 Combine like terms: 7.25 + 2.640625 = 9.890625 2.640625 + -3.25x + x2 = 9.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 9.890625 Calculate the square root of the right side: 3.144936406 Break this problem into two subproblems by setting (x + -1.625) equal to 3.144936406 and -3.144936406.Subproblem 1
x + -1.625 = 3.144936406 Simplifying x + -1.625 = 3.144936406 Reorder the terms: -1.625 + x = 3.144936406 Solving -1.625 + x = 3.144936406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.144936406 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.144936406 + 1.625 x = 3.144936406 + 1.625 Combine like terms: 3.144936406 + 1.625 = 4.769936406 x = 4.769936406 Simplifying x = 4.769936406Subproblem 2
x + -1.625 = -3.144936406 Simplifying x + -1.625 = -3.144936406 Reorder the terms: -1.625 + x = -3.144936406 Solving -1.625 + x = -3.144936406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.144936406 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.144936406 + 1.625 x = -3.144936406 + 1.625 Combine like terms: -3.144936406 + 1.625 = -1.519936406 x = -1.519936406 Simplifying x = -1.519936406Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.769936406, -1.519936406}
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