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Simplifying 3x2 + 2x2 + -7x + -50 = 0 Reorder the terms: -50 + -7x + 3x2 + 2x2 = 0 Combine like terms: 3x2 + 2x2 = 5x2 -50 + -7x + 5x2 = 0 Solving -50 + -7x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10 + -1.4x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1.4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.4x + x2 = 0 + 10 -1.4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.4x + x2 = 10 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 10 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 10 + 0.49 Combine like terms: 10 + 0.49 = 10.49 0.49 + -1.4x + x2 = 10.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 10.49 Calculate the square root of the right side: 3.238826948 Break this problem into two subproblems by setting (x + -0.7) equal to 3.238826948 and -3.238826948.Subproblem 1
x + -0.7 = 3.238826948 Simplifying x + -0.7 = 3.238826948 Reorder the terms: -0.7 + x = 3.238826948 Solving -0.7 + x = 3.238826948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 3.238826948 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 3.238826948 + 0.7 x = 3.238826948 + 0.7 Combine like terms: 3.238826948 + 0.7 = 3.938826948 x = 3.938826948 Simplifying x = 3.938826948Subproblem 2
x + -0.7 = -3.238826948 Simplifying x + -0.7 = -3.238826948 Reorder the terms: -0.7 + x = -3.238826948 Solving -0.7 + x = -3.238826948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -3.238826948 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -3.238826948 + 0.7 x = -3.238826948 + 0.7 Combine like terms: -3.238826948 + 0.7 = -2.538826948 x = -2.538826948 Simplifying x = -2.538826948Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.938826948, -2.538826948}
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