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Simplifying 0.75x + x * x = 50 Multiply x * x 0.75x + x2 = 50 Solving 0.75x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 0.75x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 0.75x + x2 = 0 Begin completing the square. 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 = 6.706004519 x = 6.706004519 Simplifying x = 6.706004519Subproblem 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 = -7.456004519 x = -7.456004519 Simplifying x = -7.456004519Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.706004519, -7.456004519}
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