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Simplifying 0 = 7(x * x) + -5x + -24 Multiply x * x 0 = 7(x2) + -5x + -24 Reorder the terms: 0 = -24 + -5x + 7x2 Solving 0 = -24 + -5x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + 5x + -7x2 = -24 + -5x + 7x2 + 24 + 5x + -7x2 Reorder the terms: 24 + 5x + -7x2 = -24 + 24 + -5x + 5x + 7x2 + -7x2 Combine like terms: -24 + 24 = 0 24 + 5x + -7x2 = 0 + -5x + 5x + 7x2 + -7x2 24 + 5x + -7x2 = -5x + 5x + 7x2 + -7x2 Combine like terms: -5x + 5x = 0 24 + 5x + -7x2 = 0 + 7x2 + -7x2 24 + 5x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 24 + 5x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3.428571429 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -0.7142857143x + 3.428571429 + x2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -0.7142857143x + x2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 3.428571429 -0.7142857143x + x2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -0.7142857143x + x2 = 3.428571429 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 3.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 3.428571429 + 0.1275510204 Combine like terms: 3.428571429 + 0.1275510204 = 3.5561224494 0.1275510204 + -0.7142857143x + x2 = 3.5561224494 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 3.5561224494 Calculate the square root of the right side: 1.885768398 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.885768398 and -1.885768398.Subproblem 1
x + -0.3571428572 = 1.885768398 Simplifying x + -0.3571428572 = 1.885768398 Reorder the terms: -0.3571428572 + x = 1.885768398 Solving -0.3571428572 + x = 1.885768398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.885768398 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.885768398 + 0.3571428572 x = 1.885768398 + 0.3571428572 Combine like terms: 1.885768398 + 0.3571428572 = 2.2429112552 x = 2.2429112552 Simplifying x = 2.2429112552Subproblem 2
x + -0.3571428572 = -1.885768398 Simplifying x + -0.3571428572 = -1.885768398 Reorder the terms: -0.3571428572 + x = -1.885768398 Solving -0.3571428572 + x = -1.885768398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.885768398 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.885768398 + 0.3571428572 x = -1.885768398 + 0.3571428572 Combine like terms: -1.885768398 + 0.3571428572 = -1.5286255408 x = -1.5286255408 Simplifying x = -1.5286255408Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2429112552, -1.5286255408}
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