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Simplifying 243 = 4x2 + -4x Reorder the terms: 243 = -4x + 4x2 Solving 243 = -4x + 4x2 Solving for variable 'x'. Reorder the terms: 243 + 4x + -4x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 243 + 4x + -4x2 = 0 + 4x2 + -4x2 243 + 4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 243 + 4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -60.75 + -1x + x2 = 0 Move the constant term to the right: Add '60.75' to each side of the equation. -60.75 + -1x + 60.75 + x2 = 0 + 60.75 Reorder the terms: -60.75 + 60.75 + -1x + x2 = 0 + 60.75 Combine like terms: -60.75 + 60.75 = 0.00 0.00 + -1x + x2 = 0 + 60.75 -1x + x2 = 0 + 60.75 Combine like terms: 0 + 60.75 = 60.75 -1x + x2 = 60.75 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 60.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 60.75 + 0.25 Combine like terms: 60.75 + 0.25 = 61 0.25 + -1x + x2 = 61 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -0.5) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -0.5 = 7.810249676 Simplifying x + -0.5 = 7.810249676 Reorder the terms: -0.5 + x = 7.810249676 Solving -0.5 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.810249676 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.810249676 + 0.5 x = 7.810249676 + 0.5 Combine like terms: 7.810249676 + 0.5 = 8.310249676 x = 8.310249676 Simplifying x = 8.310249676Subproblem 2
x + -0.5 = -7.810249676 Simplifying x + -0.5 = -7.810249676 Reorder the terms: -0.5 + x = -7.810249676 Solving -0.5 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.810249676 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.810249676 + 0.5 x = -7.810249676 + 0.5 Combine like terms: -7.810249676 + 0.5 = -7.310249676 x = -7.310249676 Simplifying x = -7.310249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.310249676, -7.310249676}
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