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Simplifying 4x2 + -36x = 38.75 Reorder the terms: -36x + 4x2 = 38.75 Solving -36x + 4x2 = 38.75 Solving for variable 'x'. Reorder the terms: -38.75 + -36x + 4x2 = 38.75 + -38.75 Combine like terms: 38.75 + -38.75 = 0.00 -38.75 + -36x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.6875 + -9x + x2 = 0.00 Move the constant term to the right: Add '9.6875' to each side of the equation. -9.6875 + -9x + 9.6875 + x2 = 0.00 + 9.6875 Reorder the terms: -9.6875 + 9.6875 + -9x + x2 = 0.00 + 9.6875 Combine like terms: -9.6875 + 9.6875 = 0.0000 0.0000 + -9x + x2 = 0.00 + 9.6875 -9x + x2 = 0.00 + 9.6875 Combine like terms: 0.00 + 9.6875 = 9.6875 -9x + x2 = 9.6875 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 9.6875 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 9.6875 + 20.25 Combine like terms: 9.6875 + 20.25 = 29.9375 20.25 + -9x + x2 = 29.9375 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 29.9375 Calculate the square root of the right side: 5.471517157 Break this problem into two subproblems by setting (x + -4.5) equal to 5.471517157 and -5.471517157.Subproblem 1
x + -4.5 = 5.471517157 Simplifying x + -4.5 = 5.471517157 Reorder the terms: -4.5 + x = 5.471517157 Solving -4.5 + x = 5.471517157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.471517157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.471517157 + 4.5 x = 5.471517157 + 4.5 Combine like terms: 5.471517157 + 4.5 = 9.971517157 x = 9.971517157 Simplifying x = 9.971517157Subproblem 2
x + -4.5 = -5.471517157 Simplifying x + -4.5 = -5.471517157 Reorder the terms: -4.5 + x = -5.471517157 Solving -4.5 + x = -5.471517157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.471517157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.471517157 + 4.5 x = -5.471517157 + 4.5 Combine like terms: -5.471517157 + 4.5 = -0.971517157 x = -0.971517157 Simplifying x = -0.971517157Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.971517157, -0.971517157}
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