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Simplifying 4x2 + -45x = 45 Reorder the terms: -45x + 4x2 = 45 Solving -45x + 4x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -45x + 4x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -45x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -11.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -11.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -11.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -11.25x + x2 = 0 + 11.25 -11.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -11.25x + x2 = 11.25 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = 11.25 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = 11.25 + 31.640625 Combine like terms: 11.25 + 31.640625 = 42.890625 31.640625 + -11.25x + x2 = 42.890625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 42.890625 Calculate the square root of the right side: 6.549093449 Break this problem into two subproblems by setting (x + -5.625) equal to 6.549093449 and -6.549093449.Subproblem 1
x + -5.625 = 6.549093449 Simplifying x + -5.625 = 6.549093449 Reorder the terms: -5.625 + x = 6.549093449 Solving -5.625 + x = 6.549093449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 6.549093449 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 6.549093449 + 5.625 x = 6.549093449 + 5.625 Combine like terms: 6.549093449 + 5.625 = 12.174093449 x = 12.174093449 Simplifying x = 12.174093449Subproblem 2
x + -5.625 = -6.549093449 Simplifying x + -5.625 = -6.549093449 Reorder the terms: -5.625 + x = -6.549093449 Solving -5.625 + x = -6.549093449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -6.549093449 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -6.549093449 + 5.625 x = -6.549093449 + 5.625 Combine like terms: -6.549093449 + 5.625 = -0.924093449 x = -0.924093449 Simplifying x = -0.924093449Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.174093449, -0.924093449}
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