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Simplifying 50x2 + -96x + -135 = 0 Reorder the terms: -135 + -96x + 50x2 = 0 Solving -135 + -96x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -2.7 + -1.92x + x2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -1.92x + 2.7 + x2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + -1.92x + x2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -1.92x + x2 = 0 + 2.7 -1.92x + x2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 -1.92x + x2 = 2.7 The x term is -1.92x. Take half its coefficient (-0.96). Square it (0.9216) and add it to both sides. Add '0.9216' to each side of the equation. -1.92x + 0.9216 + x2 = 2.7 + 0.9216 Reorder the terms: 0.9216 + -1.92x + x2 = 2.7 + 0.9216 Combine like terms: 2.7 + 0.9216 = 3.6216 0.9216 + -1.92x + x2 = 3.6216 Factor a perfect square on the left side: (x + -0.96)(x + -0.96) = 3.6216 Calculate the square root of the right side: 1.903050183 Break this problem into two subproblems by setting (x + -0.96) equal to 1.903050183 and -1.903050183.Subproblem 1
x + -0.96 = 1.903050183 Simplifying x + -0.96 = 1.903050183 Reorder the terms: -0.96 + x = 1.903050183 Solving -0.96 + x = 1.903050183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96' to each side of the equation. -0.96 + 0.96 + x = 1.903050183 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + x = 1.903050183 + 0.96 x = 1.903050183 + 0.96 Combine like terms: 1.903050183 + 0.96 = 2.863050183 x = 2.863050183 Simplifying x = 2.863050183Subproblem 2
x + -0.96 = -1.903050183 Simplifying x + -0.96 = -1.903050183 Reorder the terms: -0.96 + x = -1.903050183 Solving -0.96 + x = -1.903050183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96' to each side of the equation. -0.96 + 0.96 + x = -1.903050183 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + x = -1.903050183 + 0.96 x = -1.903050183 + 0.96 Combine like terms: -1.903050183 + 0.96 = -0.943050183 x = -0.943050183 Simplifying x = -0.943050183Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.863050183, -0.943050183}
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