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Simplifying 0 = 4x2 + 7x + -243 Reorder the terms: 0 = -243 + 7x + 4x2 Solving 0 = -243 + 7x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 243 = 243 243 + -7x + -4x2 = -243 + 7x + 4x2 + 243 + -7x + -4x2 Reorder the terms: 243 + -7x + -4x2 = -243 + 243 + 7x + -7x + 4x2 + -4x2 Combine like terms: -243 + 243 = 0 243 + -7x + -4x2 = 0 + 7x + -7x + 4x2 + -4x2 243 + -7x + -4x2 = 7x + -7x + 4x2 + -4x2 Combine like terms: 7x + -7x = 0 243 + -7x + -4x2 = 0 + 4x2 + -4x2 243 + -7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 243 + -7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -60.75 + 1.75x + x2 = 0 Move the constant term to the right: Add '60.75' to each side of the equation. -60.75 + 1.75x + 60.75 + x2 = 0 + 60.75 Reorder the terms: -60.75 + 60.75 + 1.75x + x2 = 0 + 60.75 Combine like terms: -60.75 + 60.75 = 0.00 0.00 + 1.75x + x2 = 0 + 60.75 1.75x + x2 = 0 + 60.75 Combine like terms: 0 + 60.75 = 60.75 1.75x + x2 = 60.75 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 60.75 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 60.75 + 0.765625 Combine like terms: 60.75 + 0.765625 = 61.515625 0.765625 + 1.75x + x2 = 61.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 61.515625 Calculate the square root of the right side: 7.843189721 Break this problem into two subproblems by setting (x + 0.875) equal to 7.843189721 and -7.843189721.Subproblem 1
x + 0.875 = 7.843189721 Simplifying x + 0.875 = 7.843189721 Reorder the terms: 0.875 + x = 7.843189721 Solving 0.875 + x = 7.843189721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 7.843189721 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 7.843189721 + -0.875 x = 7.843189721 + -0.875 Combine like terms: 7.843189721 + -0.875 = 6.968189721 x = 6.968189721 Simplifying x = 6.968189721Subproblem 2
x + 0.875 = -7.843189721 Simplifying x + 0.875 = -7.843189721 Reorder the terms: 0.875 + x = -7.843189721 Solving 0.875 + x = -7.843189721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -7.843189721 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -7.843189721 + -0.875 x = -7.843189721 + -0.875 Combine like terms: -7.843189721 + -0.875 = -8.718189721 x = -8.718189721 Simplifying x = -8.718189721Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.968189721, -8.718189721}
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