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Simplifying (2x2 + 3x + -7) + -1(-5x + 4) = 0 Reorder the terms: (-7 + 3x + 2x2) + -1(-5x + 4) = 0 Remove parenthesis around (-7 + 3x + 2x2) -7 + 3x + 2x2 + -1(-5x + 4) = 0 Reorder the terms: -7 + 3x + 2x2 + -1(4 + -5x) = 0 -7 + 3x + 2x2 + (4 * -1 + -5x * -1) = 0 -7 + 3x + 2x2 + (-4 + 5x) = 0 Reorder the terms: -7 + -4 + 3x + 5x + 2x2 = 0 Combine like terms: -7 + -4 = -11 -11 + 3x + 5x + 2x2 = 0 Combine like terms: 3x + 5x = 8x -11 + 8x + 2x2 = 0 Solving -11 + 8x + 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 + 4x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4x + x2 = 0 + 5.5 4x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4x + x2 = 5.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5.5 + 4 Reorder the terms: 4 + 4x + x2 = 5.5 + 4 Combine like terms: 5.5 + 4 = 9.5 4 + 4x + x2 = 9.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (x + 2) equal to 3.082207001 and -3.082207001.Subproblem 1
x + 2 = 3.082207001 Simplifying x + 2 = 3.082207001 Reorder the terms: 2 + x = 3.082207001 Solving 2 + x = 3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.082207001 + -2 x = 3.082207001 + -2 Combine like terms: 3.082207001 + -2 = 1.082207001 x = 1.082207001 Simplifying x = 1.082207001Subproblem 2
x + 2 = -3.082207001 Simplifying x + 2 = -3.082207001 Reorder the terms: 2 + x = -3.082207001 Solving 2 + x = -3.082207001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.082207001 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.082207001 + -2 x = -3.082207001 + -2 Combine like terms: -3.082207001 + -2 = -5.082207001 x = -5.082207001 Simplifying x = -5.082207001Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.082207001, -5.082207001}
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