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Simplifying 45 + -4x2 = x Solving 45 + -4x2 = x Solving for variable 'x'. Reorder the terms: 45 + -1x + -4x2 = x + -1x Combine like terms: x + -1x = 0 45 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 0.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 0.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 0.25x + x2 = 0 + 11.25 0.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 0.25x + x2 = 11.25 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 11.25 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 11.25 + 0.015625 Combine like terms: 11.25 + 0.015625 = 11.265625 0.015625 + 0.25x + x2 = 11.265625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (x + 0.125) equal to 3.356430396 and -3.356430396.Subproblem 1
x + 0.125 = 3.356430396 Simplifying x + 0.125 = 3.356430396 Reorder the terms: 0.125 + x = 3.356430396 Solving 0.125 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 3.356430396 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 3.356430396 + -0.125 x = 3.356430396 + -0.125 Combine like terms: 3.356430396 + -0.125 = 3.231430396 x = 3.231430396 Simplifying x = 3.231430396Subproblem 2
x + 0.125 = -3.356430396 Simplifying x + 0.125 = -3.356430396 Reorder the terms: 0.125 + x = -3.356430396 Solving 0.125 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -3.356430396 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -3.356430396 + -0.125 x = -3.356430396 + -0.125 Combine like terms: -3.356430396 + -0.125 = -3.481430396 x = -3.481430396 Simplifying x = -3.481430396Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.231430396, -3.481430396}
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