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Simplifying (2x2 + -5x + 7) + -1(4x2 + 2x + -11) = 0 Reorder the terms: (7 + -5x + 2x2) + -1(4x2 + 2x + -11) = 0 Remove parenthesis around (7 + -5x + 2x2) 7 + -5x + 2x2 + -1(4x2 + 2x + -11) = 0 Reorder the terms: 7 + -5x + 2x2 + -1(-11 + 2x + 4x2) = 0 7 + -5x + 2x2 + (-11 * -1 + 2x * -1 + 4x2 * -1) = 0 7 + -5x + 2x2 + (11 + -2x + -4x2) = 0 Reorder the terms: 7 + 11 + -5x + -2x + 2x2 + -4x2 = 0 Combine like terms: 7 + 11 = 18 18 + -5x + -2x + 2x2 + -4x2 = 0 Combine like terms: -5x + -2x = -7x 18 + -7x + 2x2 + -4x2 = 0 Combine like terms: 2x2 + -4x2 = -2x2 18 + -7x + -2x2 = 0 Solving 18 + -7x + -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'. -9 + 3.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 3.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 3.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3.5x + x2 = 0 + 9 3.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 3.5x + x2 = 9 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 9 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 9 + 3.0625 Combine like terms: 9 + 3.0625 = 12.0625 3.0625 + 3.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 1.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 1.75 = 3.473110997 Simplifying x + 1.75 = 3.473110997 Reorder the terms: 1.75 + x = 3.473110997 Solving 1.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.473110997 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.473110997 + -1.75 x = 3.473110997 + -1.75 Combine like terms: 3.473110997 + -1.75 = 1.723110997 x = 1.723110997 Simplifying x = 1.723110997Subproblem 2
x + 1.75 = -3.473110997 Simplifying x + 1.75 = -3.473110997 Reorder the terms: 1.75 + x = -3.473110997 Solving 1.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.473110997 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.473110997 + -1.75 x = -3.473110997 + -1.75 Combine like terms: -3.473110997 + -1.75 = -5.223110997 x = -5.223110997 Simplifying x = -5.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.723110997, -5.223110997}
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