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Simplifying 4x2 + -9x + 13 + -2x2 + -6x + 7 = 0 Reorder the terms: 13 + 7 + -9x + -6x + 4x2 + -2x2 = 0 Combine like terms: 13 + 7 = 20 20 + -9x + -6x + 4x2 + -2x2 = 0 Combine like terms: -9x + -6x = -15x 20 + -15x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 20 + -15x + 2x2 = 0 Solving 20 + -15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -7.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -7.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7.5x + x2 = 0 + -10 -7.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7.5x + x2 = -10 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -10 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -10 + 14.0625 Combine like terms: -10 + 14.0625 = 4.0625 14.0625 + -7.5x + x2 = 4.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (x + -3.75) equal to 2.015564437 and -2.015564437.Subproblem 1
x + -3.75 = 2.015564437 Simplifying x + -3.75 = 2.015564437 Reorder the terms: -3.75 + x = 2.015564437 Solving -3.75 + x = 2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 2.015564437 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.015564437 + 3.75 x = 2.015564437 + 3.75 Combine like terms: 2.015564437 + 3.75 = 5.765564437 x = 5.765564437 Simplifying x = 5.765564437Subproblem 2
x + -3.75 = -2.015564437 Simplifying x + -3.75 = -2.015564437 Reorder the terms: -3.75 + x = -2.015564437 Solving -3.75 + x = -2.015564437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -2.015564437 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.015564437 + 3.75 x = -2.015564437 + 3.75 Combine like terms: -2.015564437 + 3.75 = 1.734435563 x = 1.734435563 Simplifying x = 1.734435563Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.765564437, 1.734435563}
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