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Simplifying 4x2 + 30x + -75 = 0 Reorder the terms: -75 + 30x + 4x2 = 0 Solving -75 + 30x + 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'. -18.75 + 7.5x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 7.5x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 7.5x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 7.5x + x2 = 0 + 18.75 7.5x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 7.5x + x2 = 18.75 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 18.75 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 18.75 + 14.0625 Combine like terms: 18.75 + 14.0625 = 32.8125 14.0625 + 7.5x + x2 = 32.8125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 32.8125 Calculate the square root of the right side: 5.728219619 Break this problem into two subproblems by setting (x + 3.75) equal to 5.728219619 and -5.728219619.Subproblem 1
x + 3.75 = 5.728219619 Simplifying x + 3.75 = 5.728219619 Reorder the terms: 3.75 + x = 5.728219619 Solving 3.75 + x = 5.728219619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 5.728219619 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.728219619 + -3.75 x = 5.728219619 + -3.75 Combine like terms: 5.728219619 + -3.75 = 1.978219619 x = 1.978219619 Simplifying x = 1.978219619Subproblem 2
x + 3.75 = -5.728219619 Simplifying x + 3.75 = -5.728219619 Reorder the terms: 3.75 + x = -5.728219619 Solving 3.75 + x = -5.728219619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -5.728219619 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.728219619 + -3.75 x = -5.728219619 + -3.75 Combine like terms: -5.728219619 + -3.75 = -9.478219619 x = -9.478219619 Simplifying x = -9.478219619Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.978219619, -9.478219619}
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