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Simplifying 0 = -4x2 + 10x + 13 Reorder the terms: 0 = 13 + 10x + -4x2 Solving 0 = 13 + 10x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + -10x + 4x2 = 13 + 10x + -4x2 + -13 + -10x + 4x2 Reorder the terms: -13 + -10x + 4x2 = 13 + -13 + 10x + -10x + -4x2 + 4x2 Combine like terms: 13 + -13 = 0 -13 + -10x + 4x2 = 0 + 10x + -10x + -4x2 + 4x2 -13 + -10x + 4x2 = 10x + -10x + -4x2 + 4x2 Combine like terms: 10x + -10x = 0 -13 + -10x + 4x2 = 0 + -4x2 + 4x2 -13 + -10x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -13 + -10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -2.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -2.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -2.5x + x2 = 0 + 3.25 -2.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -2.5x + x2 = 3.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 3.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 3.25 + 1.5625 Combine like terms: 3.25 + 1.5625 = 4.8125 1.5625 + -2.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + -1.25) equal to 2.193741097 and -2.193741097.Subproblem 1
x + -1.25 = 2.193741097 Simplifying x + -1.25 = 2.193741097 Reorder the terms: -1.25 + x = 2.193741097 Solving -1.25 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.193741097 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.193741097 + 1.25 x = 2.193741097 + 1.25 Combine like terms: 2.193741097 + 1.25 = 3.443741097 x = 3.443741097 Simplifying x = 3.443741097Subproblem 2
x + -1.25 = -2.193741097 Simplifying x + -1.25 = -2.193741097 Reorder the terms: -1.25 + x = -2.193741097 Solving -1.25 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.193741097 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.193741097 + 1.25 x = -2.193741097 + 1.25 Combine like terms: -2.193741097 + 1.25 = -0.943741097 x = -0.943741097 Simplifying x = -0.943741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.443741097, -0.943741097}
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