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Simplifying (5x2 + 3x + -7) + -1(3x2 + -1x + 4) = 0 Reorder the terms: (-7 + 3x + 5x2) + -1(3x2 + -1x + 4) = 0 Remove parenthesis around (-7 + 3x + 5x2) -7 + 3x + 5x2 + -1(3x2 + -1x + 4) = 0 Reorder the terms: -7 + 3x + 5x2 + -1(4 + -1x + 3x2) = 0 -7 + 3x + 5x2 + (4 * -1 + -1x * -1 + 3x2 * -1) = 0 -7 + 3x + 5x2 + (-4 + 1x + -3x2) = 0 Reorder the terms: -7 + -4 + 3x + 1x + 5x2 + -3x2 = 0 Combine like terms: -7 + -4 = -11 -11 + 3x + 1x + 5x2 + -3x2 = 0 Combine like terms: 3x + 1x = 4x -11 + 4x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 -11 + 4x + 2x2 = 0 Solving -11 + 4x + 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'. -5.5 + 2x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 2x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 2x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 2x + x2 = 0 + 5.5 2x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 2x + x2 = 5.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.5 + 1 Reorder the terms: 1 + 2x + x2 = 5.5 + 1 Combine like terms: 5.5 + 1 = 6.5 1 + 2x + x2 = 6.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + 1) equal to 2.549509757 and -2.549509757.Subproblem 1
x + 1 = 2.549509757 Simplifying x + 1 = 2.549509757 Reorder the terms: 1 + x = 2.549509757 Solving 1 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.549509757 + -1 x = 2.549509757 + -1 Combine like terms: 2.549509757 + -1 = 1.549509757 x = 1.549509757 Simplifying x = 1.549509757Subproblem 2
x + 1 = -2.549509757 Simplifying x + 1 = -2.549509757 Reorder the terms: 1 + x = -2.549509757 Solving 1 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.549509757 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.549509757 + -1 x = -2.549509757 + -1 Combine like terms: -2.549509757 + -1 = -3.549509757 x = -3.549509757 Simplifying x = -3.549509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.549509757, -3.549509757}
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