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Simplifying 4x2 + 13x + -3.5 = 0 Reorder the terms: -3.5 + 13x + 4x2 = 0 Solving -3.5 + 13x + 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'. -0.875 + 3.25x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 3.25x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 3.25x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 3.25x + x2 = 0 + 0.875 3.25x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 3.25x + x2 = 0.875 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 0.875 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 0.875 + 2.640625 Combine like terms: 0.875 + 2.640625 = 3.515625 2.640625 + 3.25x + x2 = 3.515625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 3.515625 Calculate the square root of the right side: 1.875 Break this problem into two subproblems by setting (x + 1.625) equal to 1.875 and -1.875.Subproblem 1
x + 1.625 = 1.875 Simplifying x + 1.625 = 1.875 Reorder the terms: 1.625 + x = 1.875 Solving 1.625 + x = 1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 1.875 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 1.875 + -1.625 x = 1.875 + -1.625 Combine like terms: 1.875 + -1.625 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 1.625 = -1.875 Simplifying x + 1.625 = -1.875 Reorder the terms: 1.625 + x = -1.875 Solving 1.625 + x = -1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -1.875 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -1.875 + -1.625 x = -1.875 + -1.625 Combine like terms: -1.875 + -1.625 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -3.5}
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