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Simplifying 4x2 + 7x = 18 Reorder the terms: 7x + 4x2 = 18 Solving 7x + 4x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 7x + 4x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.75x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.75x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.75x + x2 = 0 + 4.5 1.75x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.75x + x2 = 4.5 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 = 4.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 4.5 + 0.765625 Combine like terms: 4.5 + 0.765625 = 5.265625 0.765625 + 1.75x + x2 = 5.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 5.265625 Calculate the square root of the right side: 2.294694969 Break this problem into two subproblems by setting (x + 0.875) equal to 2.294694969 and -2.294694969.Subproblem 1
x + 0.875 = 2.294694969 Simplifying x + 0.875 = 2.294694969 Reorder the terms: 0.875 + x = 2.294694969 Solving 0.875 + x = 2.294694969 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 = 2.294694969 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.294694969 + -0.875 x = 2.294694969 + -0.875 Combine like terms: 2.294694969 + -0.875 = 1.419694969 x = 1.419694969 Simplifying x = 1.419694969Subproblem 2
x + 0.875 = -2.294694969 Simplifying x + 0.875 = -2.294694969 Reorder the terms: 0.875 + x = -2.294694969 Solving 0.875 + x = -2.294694969 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 = -2.294694969 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.294694969 + -0.875 x = -2.294694969 + -0.875 Combine like terms: -2.294694969 + -0.875 = -3.169694969 x = -3.169694969 Simplifying x = -3.169694969Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.419694969, -3.169694969}
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