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Simplifying 4x2 + 15x + -75 = 0 Reorder the terms: -75 + 15x + 4x2 = 0 Solving -75 + 15x + 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 + 3.75x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 3.75x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 3.75x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 3.75x + x2 = 0 + 18.75 3.75x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 3.75x + x2 = 18.75 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 18.75 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 18.75 + 3.515625 Combine like terms: 18.75 + 3.515625 = 22.265625 3.515625 + 3.75x + x2 = 22.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 22.265625 Calculate the square root of the right side: 4.718646522 Break this problem into two subproblems by setting (x + 1.875) equal to 4.718646522 and -4.718646522.Subproblem 1
x + 1.875 = 4.718646522 Simplifying x + 1.875 = 4.718646522 Reorder the terms: 1.875 + x = 4.718646522 Solving 1.875 + x = 4.718646522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 4.718646522 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 4.718646522 + -1.875 x = 4.718646522 + -1.875 Combine like terms: 4.718646522 + -1.875 = 2.843646522 x = 2.843646522 Simplifying x = 2.843646522Subproblem 2
x + 1.875 = -4.718646522 Simplifying x + 1.875 = -4.718646522 Reorder the terms: 1.875 + x = -4.718646522 Solving 1.875 + x = -4.718646522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -4.718646522 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -4.718646522 + -1.875 x = -4.718646522 + -1.875 Combine like terms: -4.718646522 + -1.875 = -6.593646522 x = -6.593646522 Simplifying x = -6.593646522Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.843646522, -6.593646522}
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