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Simplifying 4x2 + -3x + -200 = 0 Reorder the terms: -200 + -3x + 4x2 = 0 Solving -200 + -3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -50 + -0.75x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -0.75x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -0.75x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -0.75x + x2 = 0 + 50 -0.75x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -0.75x + x2 = 50 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 50 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 50 + 0.140625 Combine like terms: 50 + 0.140625 = 50.140625 0.140625 + -0.75x + x2 = 50.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 50.140625 Calculate the square root of the right side: 7.081004519 Break this problem into two subproblems by setting (x + -0.375) equal to 7.081004519 and -7.081004519.Subproblem 1
x + -0.375 = 7.081004519 Simplifying x + -0.375 = 7.081004519 Reorder the terms: -0.375 + x = 7.081004519 Solving -0.375 + x = 7.081004519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 7.081004519 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 7.081004519 + 0.375 x = 7.081004519 + 0.375 Combine like terms: 7.081004519 + 0.375 = 7.456004519 x = 7.456004519 Simplifying x = 7.456004519Subproblem 2
x + -0.375 = -7.081004519 Simplifying x + -0.375 = -7.081004519 Reorder the terms: -0.375 + x = -7.081004519 Solving -0.375 + x = -7.081004519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -7.081004519 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -7.081004519 + 0.375 x = -7.081004519 + 0.375 Combine like terms: -7.081004519 + 0.375 = -6.706004519 x = -6.706004519 Simplifying x = -6.706004519Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.456004519, -6.706004519}
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