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Simplifying 4x2 + 15x + 13 = 0 Reorder the terms: 13 + 15x + 4x2 = 0 Solving 13 + 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'. 3.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 3.75x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 3.75x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 3.75x + x2 = 0 + -3.25 3.75x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 3.75x + x2 = -3.25 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 = -3.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -3.25 + 3.515625 Combine like terms: -3.25 + 3.515625 = 0.265625 3.515625 + 3.75x + x2 = 0.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + 1.875) equal to 0.515388203 and -0.515388203.Subproblem 1
x + 1.875 = 0.515388203 Simplifying x + 1.875 = 0.515388203 Reorder the terms: 1.875 + x = 0.515388203 Solving 1.875 + x = 0.515388203 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 = 0.515388203 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 0.515388203 + -1.875 x = 0.515388203 + -1.875 Combine like terms: 0.515388203 + -1.875 = -1.359611797 x = -1.359611797 Simplifying x = -1.359611797Subproblem 2
x + 1.875 = -0.515388203 Simplifying x + 1.875 = -0.515388203 Reorder the terms: 1.875 + x = -0.515388203 Solving 1.875 + x = -0.515388203 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 = -0.515388203 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -0.515388203 + -1.875 x = -0.515388203 + -1.875 Combine like terms: -0.515388203 + -1.875 = -2.390388203 x = -2.390388203 Simplifying x = -2.390388203Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.359611797, -2.390388203}
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