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Simplifying -2x2 + -3x + 50 = 0 Reorder the terms: 50 + -3x + -2x2 = 0 Solving 50 + -3x + -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'. -25 + 1.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 1.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 1.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 1.5x + x2 = 0 + 25 1.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 1.5x + x2 = 25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 25 + 0.5625 Combine like terms: 25 + 0.5625 = 25.5625 0.5625 + 1.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 0.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 0.75 = 5.055937104 Simplifying x + 0.75 = 5.055937104 Reorder the terms: 0.75 + x = 5.055937104 Solving 0.75 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.055937104 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.055937104 + -0.75 x = 5.055937104 + -0.75 Combine like terms: 5.055937104 + -0.75 = 4.305937104 x = 4.305937104 Simplifying x = 4.305937104Subproblem 2
x + 0.75 = -5.055937104 Simplifying x + 0.75 = -5.055937104 Reorder the terms: 0.75 + x = -5.055937104 Solving 0.75 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.055937104 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.055937104 + -0.75 x = -5.055937104 + -0.75 Combine like terms: -5.055937104 + -0.75 = -5.805937104 x = -5.805937104 Simplifying x = -5.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.305937104, -5.805937104}
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