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Simplifying 4x2 + 15x + -40 = 0 Reorder the terms: -40 + 15x + 4x2 = 0 Solving -40 + 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'. -10 + 3.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 3.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 3.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3.75x + x2 = 0 + 10 3.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 3.75x + x2 = 10 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 = 10 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 10 + 3.515625 Combine like terms: 10 + 3.515625 = 13.515625 3.515625 + 3.75x + x2 = 13.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 13.515625 Calculate the square root of the right side: 3.676360292 Break this problem into two subproblems by setting (x + 1.875) equal to 3.676360292 and -3.676360292.Subproblem 1
x + 1.875 = 3.676360292 Simplifying x + 1.875 = 3.676360292 Reorder the terms: 1.875 + x = 3.676360292 Solving 1.875 + x = 3.676360292 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 = 3.676360292 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 3.676360292 + -1.875 x = 3.676360292 + -1.875 Combine like terms: 3.676360292 + -1.875 = 1.801360292 x = 1.801360292 Simplifying x = 1.801360292Subproblem 2
x + 1.875 = -3.676360292 Simplifying x + 1.875 = -3.676360292 Reorder the terms: 1.875 + x = -3.676360292 Solving 1.875 + x = -3.676360292 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 = -3.676360292 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -3.676360292 + -1.875 x = -3.676360292 + -1.875 Combine like terms: -3.676360292 + -1.875 = -5.551360292 x = -5.551360292 Simplifying x = -5.551360292Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.801360292, -5.551360292}
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