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Simplifying 0.5x + x + (x + -35)(x + -46) = 360 Reorder the terms: 0.5x + x + (-35 + x)(x + -46) = 360 Reorder the terms: 0.5x + x + (-35 + x)(-46 + x) = 360 Multiply (-35 + x) * (-46 + x) 0.5x + x + (-35(-46 + x) + x(-46 + x)) = 360 0.5x + x + ((-46 * -35 + x * -35) + x(-46 + x)) = 360 0.5x + x + ((1610 + -35x) + x(-46 + x)) = 360 0.5x + x + (1610 + -35x + (-46 * x + x * x)) = 360 0.5x + x + (1610 + -35x + (-46x + x2)) = 360 Combine like terms: -35x + -46x = -81x 0.5x + x + (1610 + -81x + x2) = 360 Reorder the terms: 1610 + 0.5x + x + -81x + x2 = 360 Combine like terms: 0.5x + x = 1.5x 1610 + 1.5x + -81x + x2 = 360 Combine like terms: 1.5x + -81x = -79.5x 1610 + -79.5x + x2 = 360 Solving 1610 + -79.5x + x2 = 360 Solving for variable 'x'. Reorder the terms: 1610 + -360 + -79.5x + x2 = 360 + -360 Combine like terms: 1610 + -360 = 1250 1250 + -79.5x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 1250 + -79.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1250' to each side of the equation. 1250 + -79.5x + -1250 + x2 = 0 + -1250 Reorder the terms: 1250 + -1250 + -79.5x + x2 = 0 + -1250 Combine like terms: 1250 + -1250 = 0 0 + -79.5x + x2 = 0 + -1250 -79.5x + x2 = 0 + -1250 Combine like terms: 0 + -1250 = -1250 -79.5x + x2 = -1250 The x term is -79.5x. Take half its coefficient (-39.75). Square it (1580.0625) and add it to both sides. Add '1580.0625' to each side of the equation. -79.5x + 1580.0625 + x2 = -1250 + 1580.0625 Reorder the terms: 1580.0625 + -79.5x + x2 = -1250 + 1580.0625 Combine like terms: -1250 + 1580.0625 = 330.0625 1580.0625 + -79.5x + x2 = 330.0625 Factor a perfect square on the left side: (x + -39.75)(x + -39.75) = 330.0625 Calculate the square root of the right side: 18.167622299 Break this problem into two subproblems by setting (x + -39.75) equal to 18.167622299 and -18.167622299.Subproblem 1
x + -39.75 = 18.167622299 Simplifying x + -39.75 = 18.167622299 Reorder the terms: -39.75 + x = 18.167622299 Solving -39.75 + x = 18.167622299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.75' to each side of the equation. -39.75 + 39.75 + x = 18.167622299 + 39.75 Combine like terms: -39.75 + 39.75 = 0.00 0.00 + x = 18.167622299 + 39.75 x = 18.167622299 + 39.75 Combine like terms: 18.167622299 + 39.75 = 57.917622299 x = 57.917622299 Simplifying x = 57.917622299Subproblem 2
x + -39.75 = -18.167622299 Simplifying x + -39.75 = -18.167622299 Reorder the terms: -39.75 + x = -18.167622299 Solving -39.75 + x = -18.167622299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.75' to each side of the equation. -39.75 + 39.75 + x = -18.167622299 + 39.75 Combine like terms: -39.75 + 39.75 = 0.00 0.00 + x = -18.167622299 + 39.75 x = -18.167622299 + 39.75 Combine like terms: -18.167622299 + 39.75 = 21.582377701 x = 21.582377701 Simplifying x = 21.582377701Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.917622299, 21.582377701}
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