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Simplifying 7x + -1x2 = 3.75 Solving 7x + -1x2 = 3.75 Solving for variable 'x'. Reorder the terms: -3.75 + 7x + -1x2 = 3.75 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 -3.75 + 7x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3.75 + -7x + x2 = 0.00 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -7x + -3.75 + x2 = 0.00 + -3.75 Reorder the terms: 3.75 + -3.75 + -7x + x2 = 0.00 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -7x + x2 = 0.00 + -3.75 -7x + x2 = 0.00 + -3.75 Combine like terms: 0.00 + -3.75 = -3.75 -7x + x2 = -3.75 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -3.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -3.75 + 12.25 Combine like terms: -3.75 + 12.25 = 8.5 12.25 + -7x + x2 = 8.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + -3.5) equal to 2.915475947 and -2.915475947.Subproblem 1
x + -3.5 = 2.915475947 Simplifying x + -3.5 = 2.915475947 Reorder the terms: -3.5 + x = 2.915475947 Solving -3.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.915475947 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.915475947 + 3.5 x = 2.915475947 + 3.5 Combine like terms: 2.915475947 + 3.5 = 6.415475947 x = 6.415475947 Simplifying x = 6.415475947Subproblem 2
x + -3.5 = -2.915475947 Simplifying x + -3.5 = -2.915475947 Reorder the terms: -3.5 + x = -2.915475947 Solving -3.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.915475947 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.915475947 + 3.5 x = -2.915475947 + 3.5 Combine like terms: -2.915475947 + 3.5 = 0.584524053 x = 0.584524053 Simplifying x = 0.584524053Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.415475947, 0.584524053}
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