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Simplifying 4x2 + 7x + -72 = 0 Reorder the terms: -72 + 7x + 4x2 = 0 Solving -72 + 7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18 + 1.75x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 1.75x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 1.75x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 1.75x + x2 = 0 + 18 1.75x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 1.75x + x2 = 18 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 = 18 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 18 + 0.765625 Combine like terms: 18 + 0.765625 = 18.765625 0.765625 + 1.75x + x2 = 18.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 18.765625 Calculate the square root of the right side: 4.331930863 Break this problem into two subproblems by setting (x + 0.875) equal to 4.331930863 and -4.331930863.Subproblem 1
x + 0.875 = 4.331930863 Simplifying x + 0.875 = 4.331930863 Reorder the terms: 0.875 + x = 4.331930863 Solving 0.875 + x = 4.331930863 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 = 4.331930863 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 4.331930863 + -0.875 x = 4.331930863 + -0.875 Combine like terms: 4.331930863 + -0.875 = 3.456930863 x = 3.456930863 Simplifying x = 3.456930863Subproblem 2
x + 0.875 = -4.331930863 Simplifying x + 0.875 = -4.331930863 Reorder the terms: 0.875 + x = -4.331930863 Solving 0.875 + x = -4.331930863 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 = -4.331930863 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -4.331930863 + -0.875 x = -4.331930863 + -0.875 Combine like terms: -4.331930863 + -0.875 = -5.206930863 x = -5.206930863 Simplifying x = -5.206930863Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.456930863, -5.206930863}
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