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Simplifying 4x2 + 15x + 12 = 0 Reorder the terms: 12 + 15x + 4x2 = 0 Solving 12 + 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 + 3.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.75x + x2 = 0 + -3 3.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.75x + x2 = -3 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 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = -3 + 3.515625 Combine like terms: -3 + 3.515625 = 0.515625 3.515625 + 3.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + 1.875) equal to 0.718070331 and -0.718070331.Subproblem 1
x + 1.875 = 0.718070331 Simplifying x + 1.875 = 0.718070331 Reorder the terms: 1.875 + x = 0.718070331 Solving 1.875 + x = 0.718070331 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 = 0.718070331 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 0.718070331 + -1.875 x = 0.718070331 + -1.875 Combine like terms: 0.718070331 + -1.875 = -1.156929669 x = -1.156929669 Simplifying x = -1.156929669Subproblem 2
x + 1.875 = -0.718070331 Simplifying x + 1.875 = -0.718070331 Reorder the terms: 1.875 + x = -0.718070331 Solving 1.875 + x = -0.718070331 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 = -0.718070331 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -0.718070331 + -1.875 x = -0.718070331 + -1.875 Combine like terms: -0.718070331 + -1.875 = -2.593070331 x = -2.593070331 Simplifying x = -2.593070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.156929669, -2.593070331}
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